第三次上机试验报告

1、2011029170002王柳一、实验内容：(1) 对高阶多多项式20 p(x)=(x-1)(x-2)|H(x-20)®U (x-k)k丄编程求下面方程的解19p(x) ；x =0并绘图演示方程的解与扰动量；的关系。(2) 对n =220，生成对应的Hilbert 矩阵，计算矩阵的条件数；通过先确定解获得常向量b的方法,确定方程组Hnx =b最后，用矩阵分解方法求解方程组，并分析计算结果(3)对函数f (x)二11 25x2的 Chebyshev点xk = cos(2k-1)二2(n 1)k 1,2,., n 1编程进行Lagrange插值，并分析插值结果、实验程序:实验一：>

2、> X=zeros(20,50);>> ve=zeros(1,21);>> ess=li nspace(0,0.00001,50);k=1;>> while k<=50ve(2)=ess(k);X(1:20,k)=roots(poly(1:20)+ve); k=k+1;end>> m=1;>> while m<=20figure(m),plot(ess,X(m,:); m=m+1;end实验二：>> n=2;>> A=zeros(20,20);>> while *=20x=1: n

3、;H=hilb( n);b=H*x'L U=lu(H);y=Lb;X=Uy;A( n,1: n)=x-X'n=n+1;end实验三：程序1:for a=1:10b=a+1;for c=1:bX(c)=cos(2*c-1)*pi/2/(a+1);Y(c)=1/(1+25*X(c)A2);x=-1:0.05:1;endm=le ngth(x);for i=1:mz=x(i);s=0;for k=1:bL=1;for j=1:bif j=k L=L*(z-X(j)/(X(k)-X(j); end ends=s+L*Y(k);endy(i)=s;endfigure(1)plot(x,y

4、,'r');hold on;figure(2)plot(X,Y,'b*')hold onend程序2:for a=2:2:10b=a+1;X=li nspace(-1,1,b);Y=1./(1+25*X.A2);x=-1:0.05:1;m=le ngth(x);for i=1:mz=x(i);s=0;for k=1:bL=1;for j=1:bif j=kL=L*(z-X(j)/(X(k)-X(j);endends=s+L*Y(k);endy(i)=s；end figure(1) plot(x,y,'r'); hold on;figure(2)

5、plot(X,Y,'b*') hold on end三、实验结果: 实验一、xlO'10'百IIIIID01.2D.4O.EQS11.2x 10U.20.4m.EDS11.2斗 LJiIio.2a.4 q.e os i 1.2xW1实验二、A =1.0e+003Colum ns 1 through 100000000000-0.00000.000000000000-0.00000.0000-0.00000000000-0.00000.0000-0.00000.00000000000.0000-0.00000.0000-0.0000 0.0000000000.00

6、00-0.00000.0000-0.00000.0000-0.000000000.0000-0.00000.0000-0.00000.0000-0.00000.0000000-0.00000.0000-0.0000 0.0000 -0.00000.0000-0.00000.000000-0.00000.0000-0.0000 0.0000 -0.00000.0000-0.00000.0000-0.00000-0.00000.0000-0.0000 0.0000 -0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.0000 0.0000

7、-0.00000.0000-0.00000.0000-0.00000.0000-0.00000.0000-0.0000 0.0000 -0.00000.0001-0.00030.0006-0.00070.00050.0000-0.00000.0000-0.00010.0005-0.00270.0096-0.02230.0348-0.03610.0000-0.00000.0000-0.00040.0030-0.00980.00800.0593-0.25700.51540.0000-0.00000.0000-0.00010.0005-0.00290.0095-0.01710.00860.03470

8、.0000-0.00000.0000-0.00000.0003-0.00160.0059-0.01330.01450.00940.0000-0.00000.0000-0.00010.0009-0.00420.0118-0.01820.00820.01850.00000.0000-0.00000.0002-0.00270.0187-0.07620.1806-0.22490.08130.00000.0000-0.00000.0001-0.00170.0120-0.04970.1224-0.16990.10640.0000-0.00000.0000-0.00030.0028-0.01370.0371

9、-0.0464-0.01640.1243Columns 11 through 200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-0.0000000000000-0.00020.0000000000000.0238-0.00910.00150000000-0.60910.4336-0.17270.0296000000-0.09440.1170-0.08240.0318-0.005300000-0.06240.1107-0.11100.0674-0.02320.00350000-0.02890.00590.01030.0082-0.02630.0181-0.00420000.05240.1690-0.3743-0.18621.0944-1.21710.6004-0.115600-0.03270.1652-0.3051-0.04850.7195-0.93870.5714-0.16990.01910-0.1120 -0.04210.08830.0222-0.06280.1013-0.29020.3783-0