数值分析拟合MATLAB代码

1、第二章 第一题MATLAB代码：%用spline作图xi=0.2 0.4 0.6 0.8 1.0;yi=0.98 0.92 0.81 0.64 0.38;x=-1:0.01:2;y1=Newton3(xi,yi,x; %源代码见m文件y2=spline(xi,yi,x;plot(xi,yi,'o',x,y1,'r-',x,y2,'k'%用csape作图xi=0.2 0.4 0.6 0.8 1.0;yi=0.98 0.92 0.81 0.64 0.38;x=-1:0.01:2;y1=Newton3(xi,yi,x; %源代码见m文件pp=csape

2、(xi,yi, 'variational'y2=ppval(pp,x;plot(xi,yi,'o',x,y1,'r-',x,y2,'k'% Newton3function f=Newton3(x,y,x0syms t;if(length(x=length(yn=length(x;c(1:n=0.0;elsedisp('x和y维数不相等'return;endf=y(1;y1=0;l=1;for(i=1:n-1for(j=i+1:ny1(j=(y(j-y(i/(x(j-x(i;endc(i=y1(i+1;l=l*(t-

3、x(i;f=f+c(i*l;simplify(f;y=y1;if(i=n-1if(nargin=3f=subs(f,'t',x0;elsef=collect(f;f=vpa(f,6;endendend第二题MATLAB代码：y1=zeros(1,11;x1=-1:0.2:1;for i=1:11,p=1./(1+25.*x1(i.2;y1(i=p;endx=-1:0.01:1;ym=language(x1,y1,x;yn=spline(x1,y1,x;y2=zeros(1,21;x2=-1:0.1:1;for i=1:21,p=1./(1+25.*x2(i.2;y2(i=p;e

4、ndx=-1:0.01:1;yi=language(x2,y2,x;yj=spline(x2,y2,x;figure(1;plot(x1,y1,'o',x,ym,'r-',x,yn,'k-'figure(2;plot(x2,y2,'o',x,yi,'r-',x,yj,'k-'% Languagefunction f =Language(x,y,x0syms t;if(length(x=length(yn=length(x;elsedisp('x和y的维数不相等！'return;end

5、f=0.0;for(i=1:nl=y(i;for(j=1:i-1l=l*(t-x(j/(x(i-x(j;end;for(j=i+1:nl=l*(t-x(j/(x(i-x(j;endf=f+l;simplify(f;if(i=nif(nargin=3f=subs(f,'t',x0;elsef=collect(f;f=vpa(f,6;endendend 第三题MATLAB代码：用spline进行插值x1=0 1 4 9 16 25 36 49 64 ;y1=0 1 2 3 4 5 6 7 8;x=0:0.1:64;ym=language(x1,y1,x;yn=spline(x1,y

6、1,x;figure(1;plot(x1,y1,'o',x,ym,'k-',x,yn,'r-'用scape用第一边界条件进行插值x1=0 1 4 9 16 25 36 49 64 ;y1=0 1 2 3 4 5 6 7 8;x=0:0.1:64;ym=language(x1,y1,x; %原函数见上面pp=csape(x1,y1, 'complete',0.2,-1; yn=ppval(pp,x;figure(1;plot(x1,y1,'o',x,ym,'k-',x,yn,'r-'结

7、论：0 64三次样条插值精确0 1多项式插值精确第三章第一题MATLAB代码：y=zeros(1,11;x=-1:0.2:1;for i=1:11,p=1./(1+25.*x(i.2;y(i=p;endA=polyfit(x,y,10;y1=poly2str(A,'x'p1=-1:0.02:1;u1=polyval(A,p1;plot(p1,u1,x,y,'o'y1y1 =1.5271 x3 + 3.8235 x2 + 3.2599 x + 1.0023第二题MATLAB代码：x=0.0 0.1 0.2 0.3 0.5 0.8 1.0;y=1.0 0.41 0.

8、50 0.61 0.91 2.02 2.46;A1=polyfit(x,y,3;A2=polyfit(x,y,4;%用y=a*exp(b*x拟合u=log(y;A3=polyfit(x,u,1;m=A3(1;n=A3(2;a=exp(n;p1=-0.5:0.01:1.5;u3=a*exp(m*p1;u1=polyval(A1,p1;u2=polyval(A2,p1;plot(p1,u1,'c-',p1,u2,'r-',p1,u3,'k-.',x,y,'o'下面给定的是聊城最近1个月早晨7:00左右(北京时间的天气预报所得到的温度数

9、据表，按照数据找出任意次曲线拟合方程和它的图像。(2008年10月2611月26天数12345678910温度51415161815151855天数11121314151617181920温度347212412105天数21222324252627282930温度79121379551811下面应用Matlab编程对上述数据进行最小二乘拟合x=1:1:30;>> y=5 14 15 16 18 15 15 18 5 5 3 4 7 2 1 2 4 12 10 5 7 9 12 13 7 9 5 5 18 11 ;>> a1=polyfit(x,y,3 %三次多项式拟合%a2= polyfit(x,y,9 %九次多项式拟合%a3= polyfit(x,y,15 %十五次多项式拟合%b1= polyval(a1,xb2= polyval(a2,xb3= polyval(a3,xr1= sum(y-b1.2 %三次多项式误差平方和%r2= sum(y-b2.2 %九次次多项式误差平方和%r3= sum(y-b3.2 %十五次多项式误差平方和%plot(x,y,'*' %用*画出x,y图像%hold onplot(x,b1, 'r' %用红色线画出x,b1图像%h