gauss在matlab的程序编写.doc

1. 高斯消元法function x=mgauss(A,b,flag)ticif nargin r=rand(n);a=r*r+n*eye(n);b=a*ones(n,1); x=mgauss(a,b)Elapsed time is 0.000000 seconds.x = 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 n=100;r=rand(n);a=r*r+n*eye(n);b=a*ones(n,1);x=mgauss(a,b)Elapsed time is 0.015000 seconds.x = 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000function RA,RB,x=gaus(A,b,flag)ticif nargin0disp(请注意：因为RA=RB，所以此方程组无解.)returnendif RA=RB if RA=ndisp(请注意：因为RA=RB=n，所以此方程组有唯一解.) for k=1:(n-1) m=A(k+1:n,k)/A(k,k); A(k+1:n,k+1:n)=A(k+1:n,k+1:n)-m*A(k,k+1:n); b(k+1:n)=b(k+1:n)-m*b(k); A(k+1:n,k)=zeros(n-k,1); if flag=0,Ab=A,b,endendx=zeros(n,1);x(n)=b(n)/A(n,n);for k=n-1:-1:1 x(k)=(b(k)-A(k,k+1:n)*x(k+1:n)/A(k,k); end elsedisp(请注意：因为RA=RBn，所以此方程组有无穷多解.) endendtoc 程序验证 n=100; r=rand(n);a=r*r+n*eye(n);b=a*ones(n,1);ra,rb,x=gaus(a,b)请注意：因为RA=RB=n，所以此方程组有唯一解.Elapsed time is 0.032000 seconds.ra = 100rb = 100x = 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000图形2. LU分解程序functionl,u,x=mlu(a,b)ticn=length(b);l=zeros(n);u=zeros(n);x=zeros(n,1);y=zeros(n,1);for k=1:n u(k,k:n)=a(k,k:n)-l(k,1:k-1)*u(1:k-1,k:n); l(k:n,k)=(a(k:n,k)-l(k:n,1:k-1)*u(1:k-1,k)/u(k,k); l(k,k)=1;endfor k=1:n y(k)=b(k)-l(k,1:k-1)*y(1:k-1);endfor k=n:-1:1 x(k)=(y(k)-u(k,k+1:n)*x(k+1:n)/u(k,k);endtoc验证 n=6,r=rand(n),a=r*r+n*eye(n);b=a*ones(n,1);l,u,x=mlu(a,b)n = 6r = 0.8462 0.6813 0.3046 0.1509 0.4966 0.3420 0.5252 0.3795 0.1897 0.6979 0.8998 0.2897 0.2026 0.8318 0.1934 0.3784 0.8216 0.3412 0.6721 0.5028 0.6822 0.8600 0.6449 0.5341 0.8381 0.7095 0.3028 0.8537 0.8180 0.7271 0.0196 0.4289 0.5417 0.5936 0.6602 0.3093Elapsed time is 0.000000 seconds.l = 1.0000 0 0 0 0 0 0.2303 1.0000 0 0 0 0 0.1367 0.1246 1.0000 0 0 0 0.2291 0.1977 0.1438 1.0000 0 0 0.2676 0.2622 0.1441 0.2122 1.0000 0 0.1814 0.1540 0.0926 0.1288 0.1104 1.0000u = 8.1875 1.8854 1.1195 1.8760 2.1912 1.4851 0 7.8060 0.9728 1.5430 2.0464 1.2018 0 0 6.7424 0.9694 0.9715 0.6243 0 0 0 7.5994 1.6123 0.9789 0 0 0 0 7.6472 0.8441 0 0 0 0 0 6.4954x = 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000n=90,r=rand(n),a=r*r+n*eye(n);b=a*ones(n,1);l,u,x=mlu(a,b)n = 90r = Columns 1 through 9 0.8385 0.0164 0.4199 0.2731 0.8518 0.6859 0.8686 0.5152 0.1930 0.5681 0.1901 0.7537 0.6262 0