线性最小二乘法拟合
《MATLAB程序设计实践》课程考核
一, 实现以下科学计算算法,并举一例应用之。，参考书籍《精通MATLAB科学计
算》,王正林等著,电子工业出版社,2009年，
“线性最小二乘法拟合”
解答:
一, 最小二乘法拟合;
方法介绍
在科学实验的统计方法研究中,往往要从一组实验数据，xi,yi，中寻找出自变量x和
因变量y之间的关系y,f，x，。由于观测数据往往不准确,因此并不要求y,f，x，
经过所有的点，xi,yi，,而只要求在给定的点xi上误差ð,f，xi，,yi按照某种标准
达到最小,通常采用欧氏范数ð^2作为误差量度的标准。这就是所谓的最小二乘法。
MATLAB实现
在MATLAB中实现最小二乘法拟合通常可以采用如下途径:
利用polyfit函数进行多项式拟合。
polyfit函数源程序:
function [p,S,mu] = polyfit(x,y,n)
%POLYFIT Fit polynomial to data.
% P = POLYFIT(X,Y,N) finds the coefficients of a polynomial P(X) of % degree N that fits the data Y best in a least-squares sense. P is a
% row vector of length N+1 containing the polynomial coefficients in
% descending powers, P(1)*X^N + P(2)*X^(N-1) +...+ P(N)*X + P(N+1). %
% [P,S] = POLYFIT(X,Y,N) returns the polynomial coefficients P and a
% structure S for use with POLYVAL to obtain error estimates for % predictions. S contains fields for the triangular factor (R) from a QR
% decomposition of the Vandermonde matrix of X, the degrees of freedom
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
% (df), and the norm of the residuals (normr). If the data Y are random,
% an estimate of the covariance matrix of P is
(Rinv*Rinv')*normr^2/df,
% where Rinv is the inverse of R.
%
% [P,S,MU] = POLYFIT(X,Y,N) finds the coefficients of a polynomial in
% XHAT = (X-MU(1))/MU(2) where MU(1) = MEAN(X) and MU(2) = STD(X). This
% centering and scaling transformation improves the numerical properties
% of both the polynomial and the fitting algorithm. %
% Warning messages result if N is >= length(X), if X has repeated, or
% nearly repeated, points, or if X might need centering and scaling. %
% Class support for inputs X,Y:
% float: double, single
%
% See also POLY, POLYVAL, ROOTS.
% Copyright 1984-2004 The MathWorks, Inc.
% $Revision: 5.17.4.5 $ $Date: 2004/07/05 17:01:37 $
% The regression problem is formulated in matrix format as: %
% y = V*p or
%
% 3 2
% y = [x x x 1] [p3
% p2
% p1
% p0]
%
% where the vector p contains the coefficients to be found. For a % 7th order polynomial, matrix V would be:
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
%
% V = [x.^7 x.^6 x.^5 x.^4 x.^3 x.^2 x ones(size(x))];
if ~isequal(size(x),size(y))
error('MATLAB:polyfit:XYSizeMismatch',...
'X and Y vectors must be the same size.') end
x = x(:);
y = y(:);
if nargout > 2
mu = [mean(x); std(x)];
x = (x - mu(1))/mu(2);
end
% Construct Vandermonde matrix.
V(:,n+1) = ones(length(x),1,class(x));
for j = n:-1:1
V(:,j) = x.*V(:,j+1);
end
% Solve least squares problem.
[Q,R] = qr(V,0);
ws = warning('off','all');
p = R\(Q'*y); % Same as p = V\y;
warning(ws);
if size(R,2) > size(R,1)
warning('MATLAB:polyfit:PolyNotUnique', ...
'Polynomial is not unique; degree >= number of data points.')
elseif condest(R) > 1.0e10
if nargout > 2
warning('MATLAB:polyfit:RepeatedPoints', ...
'Polynomial is badly conditioned. Remove repeated data
points.')
else
warning('MATLAB:polyfit:RepeatedPointsOrRescale', ...
['Polynomial is badly conditioned. Remove repeated data
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
points\n' ...
' or try centering and scaling as described in HELP POLYFIT.'])
end
end
r = y - V*p;
p = p.'; % Polynomial coefficients are row vectors by convention.
% S is a structure containing three elements: the triangular factor from a
% QR decomposition of the Vandermonde matrix, the degrees of freedom and
% the norm of the residuals.
S.R = R;
S.df = length(y) - (n+1);
S.normr = norm(r);
流程图:
[例题]设y,span{1,x,x^2},用最小二乘法拟合如表所示数据。
X 0.5 1.0 1.5 2.0 2.5 3.0
y 1.75 2.45 3.81 4.80 8.00 8.60
用polyfit功能函数进行拟合。
开始 tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
流程图
输入数
据
调用polyfit
函数拟合
终止 建立m文件源代码:
function task1()
x=0.5:0.5:3.0;
y=[1.75 2.45 3.81 4.80 8.00 8.60]; a=polyfit(x,y,2)
x1=0.5:0.05:3.0
y1=a(3)+a(2)*x1+a(1)*x1.^2
plot(x,y,'*')
hold on
plot(x1,y1,'-r')
legend('实验值','拟合值')
end
在matlab命令窗口中输入:task1() 运行结果:task1()
a =
0.4900 1.2501 0.8560
x1 =
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
Columns 1 through 9
0.5000 0.5500 0.6000 0.6500 0.7000 0.7500 0.8000 0.8500 0.9000
Columns 10 through 18
0.9500 1.0000 1.0500 1.1000 1.1500 1.2000 1.2500 1.3000 1.3500
Columns 19 through 27
1.4000 1.4500 1.5000 1.5500 1.6000 1.6500 1.7000 1.7500 1.8000
Columns 28 through 36
1.8500 1.9000 1.9500 2.0000 2.0500 2.1000 2.1500 2.2000 2.2500
Columns 37 through 45
2.3000 2.3500 2.4000 2.4500 2.5000 2.5500 2.6000 2.6500 2.7000
Columns 46 through 51
2.7500 2.8000 2.8500 2.9000 2.9500 3.0000
y1 =
Columns 1 through 9
1.6036 1.6918 1.7825 1.8756 1.9712 2.0692 2.1697 2.2726 2.3780
Columns 10 through 18
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
2.4859 2.5961 2.7089 2.8241 2.9417 3.0618 3.1843 3.3093 3.4367
Columns 19 through 27
3.5666 3.6989 3.8337 3.9709 4.1106 4.2528 4.3973 4.5444 4.6939
Columns 28 through 36
4.8458 5.0002 5.1570 5.3163 5.4780 5.6422 5.8088 5.9779 6.1494
Columns 37 through 45
6.3234 6.4999 6.6787 6.8601 7.0439 7.2301 7.4188 7.6099 7.8035
Columns 46 through 51
7.9995 8.1980 8.3989 8.6023 8.8081 9.0164
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
二, 编程解决以下科学计算问题
1. 按图8-1-1所示的梯形直流电路,问
，1， 如Us=10V,求Ubc,I7,Ude
，2， 如Ude=4V,求Ubc,I7,Us
解答:此电路中设节点电压为变量,共有ua,ub,uc,ud四个。将各支路电流均用这些电压来表示.
UUUUUUU,,sbbcbccIIIIII,,,,,,,,,,,137456 RRRRRRR，，1237456
对b点和c点列出节点电流方程:I1=I3+I7,I3=I4+I6,将上述各值代入化简,得 ,, U1111s，，,,UU(1),,bcRRRRRRR，， 3127312,,
,,1111UU,，，,0(2),,bc RRRRR，33456,,
对问题，1，给出Us时,这两个方程中只有两个未知数Ub和Uc,可以写成矩阵方程
U，，s UUaaa，，，，，，，，13bb1112,,ARR，,,,,U121s,,,,,,,,,,aaUUa212223，，cc，，，，，，tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame 0,,，，
其中:a11=1/(r1+r2)+1/r3+1/r7;a12=-1/r3;a13=1/(r1+r2);
a21=1/r3;a22=-1/r3-1/(r4+r5)-1/r6; a23=0 并用矩阵左除解出Ub和Uc
再由
RU5b ,,,UUUUUI,,,,bcbcdec7
RRR，457
即可得到问题，1，的解。
对问，2，,可以推出类似的矩阵表达式,只是输入输出量不同
流程图:
开始
Ubc=u(1)-u(2) Ubc=u(1)-u(2)
Ude=u(2)*r5/(r4+r5) I7=u(1)/r7 输入Us 输入Ude
I7=u(1)/r7 Us=(r1+r2)*(u(1)*a11+u(2)*a12)
源程序代码: 代入矩阵方程 代入矩阵方程
r1=2;r2=4;r3=4;r4=4;r5=2;r6=12;r7=12; %为元件赋值
%将各系数矩阵赋值
a11=1/(r1+r2)+1/r3+1/r7;a12=-1/r3;a13=1/(r1+r2); a21=1/r3;a22=-1/r3-1/(r4+r5)-1/r6; a23=0; Us=input('Us='); % 输入解(1)的已知条件
A1=[a11,a12;a21,a22] % 列出系数矩阵A1
u=A1\[a13*Us;0] % u=[ub;uc]
Ubc=u(1)-u(2),Ude=u(2)*r5/(r4+r5),I7=u(1)/r7 % 解(1)
Ude=input('Ude='), % 输入解(2)的已知条件
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
A2=[A1,[a13;a23];0,r5/(r4+r5),0] % 列出系数矩阵A2
u=A2\[0;0;Ude], %u=[ub;uc;us] Ubc=u(1)-u(2),I7=u(1)/r7,
Us=(r1+r2)*(u(1)*a11+u(2)*a12) % 解(2)
运行结果:
输入Us=10 时, Ubc = 2.2222, Ude = 0.7407,I7 = 0.3704 输入Ude=4 时, Ubc = 12.0000, I7 = 2.0000, Us = 54.0000
如下:
task2
Us=10
A1 =
0.5000 -0.2500
0.2500 -0.5000
u =
4.4444
2.2222
Ubc =
2.2222
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
Ude =
0.7407
I7 =
0.3704
Ude=4
Ude =
4
A2 =
0.5000 -0.2500 0.1667
0.2500 -0.5000 0
0 0.3333 0
u =
24.0000
12.0000
-54.0000
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
Ubc =
12.0000
I7 =
2.0000
Us =
54.0000
>>
2.
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
，1， 差商表:
源代码:x=[4.0 5.0 6.0 7.0 8.0];
y=[2.000 2.3607 2.44949 2.64575 2.82843];
n=length(x);
newton=[x',y'];
for j=2:n
for i=n:-1:1
if i>=j
y(i)=(y(i)-y(i-1))./(x(i)-x(i-j+1));
else
y(i)=0;
end
end
newton=[newton,y'];
end
disp('下三角状的牛顿差商表如下:')
newton
运行结果:
下三角状的牛顿差商表如下:
newton =
4.0000 2.0000 0 0 0 0
5.0000 2.3607 0.3607 0 0 0
6.0000 2.4495 0.0888 -0.1360 0 0
7.0000 2.6458 0.1963 0.0537 0.0632 0
8.0000 2.8284 0.1827 -0.0068 -0.0202 -0.0209
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
>>
(2)写出牛顿多项式Nk，x，,k=1,2,3,4.
(3)在给定值x处求牛顿多项式Nk，x，,k=1,2,3,4的值。
(4)比较，3，中的结果与实际函数值。
，2，,(3),(4)编为一个程序,，2，，3，以结果表示出来,，4，以图形表示出来
流程图:
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
源程序代码:
%输入参数中x,y为元素个数相等的向量,t为待估计的点,可以为数字或向量。 %输出参数中p2为所求得的牛顿插值多项式,z为利用多项式所得的t的函数值。 x=[4 5 6 7 8];
y=[2 2.3607 2.44949 2.64575 2.82843]; t=[4.5,7.5];
n=length(x);
chaS(1)=y(1);
for i=2:n
x1=x;y1=y;
x1(i+1:n)=[];
y1(i+1:n)=[];
n1=length(x1);
s1=0;
for j=1:n1
t1=1;
for k=1:n1
if k==j
continue;
else
t1=t1*(x1(j)-x1(k));
end
end
s1=s1+y1(j)/t1;
end
chaS(i)=s1;
end
b(1,:)=[zeros(1,n-1) chaS(1)]; tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
cl=cell(1,n-1);
for i=2:n
u1=1;
for j=1:i-1
u1=conv(u1,[1 -x(j)]);
cl{i-1}=u1;
end
cl{i-1}=chaS(i)*cl{i-1};
b(i,:)=[zeros(1,n-i),cl{i-1}];
end
p2=b(1,:);
for q=2:n
p2=p2+b(q,:);
disp(strcat('牛顿',num2str(q-1),'次多项式')) vpa(poly2sym(p2),6)%显示第，2，问牛顿多项式的结果,vpa函数用于精确到小数后4位
if length(t)==1
rm=0;
for i=1:n
rm=rm+p2(i)*t^(n-i);
end
z=rm;
else
k1=length(t);
rm=zeros(1,k1);
for j=1:k1
for i=1:n
rm(j)=rm(j)+p2(i)*t(j)^(n-i);
end
z=rm;
end
end
disp(strcat('牛顿',num2str(q-1),'次多项式的值')) z %显示第，3，问给定x值处牛顿多项式的值 subplot(2,2,(q-1))
x0=0:0.01:10;
plot(x0,sqrt(x0),'-',t,z,'*') tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
title(strcat('牛顿',num2str(q-1),'次多项式不实际函数值比较'))%作图比较，3，
中结果不实际函数值
end
运行结果:
牛顿1次多项式
ans =
.360700*x+.557200
牛顿1次多项式的值
z =
2.1803 3.2625
牛顿2次多项式
ans =
-.135955*x^2+1.58430*x-2.16190
牛顿2次多项式的值
z =
2.2143 2.0728
牛顿3次多项式
ans =
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
.632300e-1*x^3-1.08440*x^2+6.26332*x-9.74950
牛顿3次多项式的值
z =
2.2380 2.9027
牛顿4次多项式
ans =
-.208512e-1*x^4+.521958*x^3-4.81678*x^2+19.5664*x-27.2646
牛顿4次多项式的值
z =
2.2576 2.7659
>>
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
牛顿1次多项式与实际函数值比较牛顿2次多项式与实际函数值比较44
33
22
11
0005100510牛顿3次多项式与实际函数值比较牛顿4次多项式与实际函数值比较44
33
22
11
0005100510
tomorrow I go fishing to the East. Bosses don't have fish to eat. "Positions out of a fat man:" going on now in the past, the Imperial Army came after eating is bad. "Old Kings Head Rush thanked the captain rushed to the base for Hong Kong, Shen Yuezhen said:" I think so well! " Aboard the ship, told through again. Months Pro happy meals freshly prepared, Scull chunks post immediately. Card that Fu sheng of the Elves take care of: "old Kings Head tomorrow, your fish such as we Captain!" "Know" this is the King's voice, by far. At night, the ship to port, next to see a few xieye of small fishing vessels, stop eating. Alex after eating two adjacent boats stopping by. Learned from the mouths of local fishermen here have is guerrilla zones, East Taihu Lake infested with bandits, Miaogang landmark, quiet at night, sometimes in the morning zhenze Japan Devils sweep, afternoon zhenze, West of guerrilla activities. Back on the boat, monthly Pro action decided by the first programme, go to Miaogang, find focal point connector. Gently open the ship, sailed into the trackless Yang. Months Pro has lost its way, don't know direction, and had to let the old King was driving. Old King pulling two oars said: "good day to see the stars, cloudy day by feel. You take a break, go to class in a 构词成分。. "No, the cabin there was" grunting ... Shout ... "snore. The next morning, Miaogang the Lion Bridge a mourning fisherman's woman. Head wrapped in white cloth, foot-wear white shoes, selling fish in a fish line. Her a red flower on the toe in his left foot, a white flower on the toe of his right foot, which is a joint sign. Women were observed on the street that a tobacco stores, posted a lot of smoke on the door, there is no old knife brand. Shopkeepers facing West, there are another two strangers looking around. Months Pro knows this focal point has been exposed, she quickly sold the fish back to the Lake, get on Board of the old King said:is Shen Yuezhen, xiaozhengxin them. A few days ago, Shen Yuezhen listen to Jones Lang LaSalle said his family had firearms, ammunition, Ding Bingcheng newly established Jiangsu Taihu Lake is in need of volunteers for the war guns and ammunition, will mobilize he offered his gun out. This small secondary progressive, PWC. Today, he leads Shen Yuezhen in backyard behind a rock. Several people quickly dug seven or eight rifles, four small pistol and some bullets, sack up, carried off the secondary courtyard. To xibaiyang, a small fishing boat approaching, Shen Yuezhen on their fishing vessel disappeared into the mist. Shen Yuezhen is a peripheral organization of the central section of the East China people's armed forces of the anti-Japanese National Salvation Association of a Communist and KMT: Wu Jiang County Government's traffic warden. She returned to her own house Dai Jia Wan, think of importation of firearms program, is afraid of diwei check months Pro frown. The next day, she came to the fishermen's uncle Wang's boat, said importation of firearms, Wang not only down, but also a good idea, brows that make the month pro stretch ... Bei Ma Yang, ship and base for Hong Kong, the Sun has been the West, the monthly Pro will kill fish, wash, place a oil sauce, cooking rice, steamed fish in the rice cooker on. Wang mentioned fish basket selling on minglilai, after the Elves when the sentry, Wang carried out from the basket of three good Mandarin fish, said with a smile: "Mister lucky, MA Yang, this is net live fish, Fu sheng's brother to try it. "The elves called Fu sheng came holding a fish said:" old Kings Head, today luck was not bad! " "Thanks to the blessing of day, only a little fish. Brothers, let me of the Ming dynasty to the North of the road Yang swings to get some fish? " "No, Ah, Eastern foreigner to prohibit! and I am not the first, not to master. "" That is a shame
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