高斯法和列主元高斯消去法解線性方程組(MATLAB版)

1、精選優(yōu)質(zhì)文檔-傾情為你奉上精選優(yōu)質(zhì)文檔-傾情為你奉上專心-專注-專業(yè)專心-專注-專業(yè)精選優(yōu)質(zhì)文檔-傾情為你奉上專心-專注-專業(yè)clear;clc;%Gauss消去法解線性方程組A=3 -5 6 4 -2 -3 8; 1 1 -9 15 1 -9 2; 2 -1 7 5 -1 6 11; -1 1 3 2 7 -1 -2; 4 3 1 -7 2 1 1; 2 9 -8 11 -1 -4 -1; 7 2 -1 2 7 -1 9;%系數(shù)矩陣b=11 2 29 9 5 8 25;%n維向量y=inv(A)*b %matlab的計(jì)算結(jié)果n=length(b);%方程個(gè)數(shù)nx=zeros(n,1);%未知

2、向量%-消去-for k=1:n-1% if A(k,k)=0;% error(Error);% end for i=k+1:n% A(i,k)=A(i,k)/A(k,k); Aik=A(i,k)/A(k,k) for j=k:n A(i,j)=A(i,j)-Aik*A(k,j); end A b(i)=b(i)-Aik*b(k) endend %-回代-x(n)=b(n)/A(n,n)for k=n-1:-1:1 S=b(k); for j=k+1:n S=S-A(k,j)*x(j); end x(k)=S/A(k,k)endx %程序的計(jì)算結(jié)果error=abs(x-ones(n,1)%誤

3、差clear;clc;%列主元Gauss校區(qū)法解線性方程組A=3 -5 6 4 -2 -3 8; 1 1 -9 15 1 -9 2; 2 -1 7 5 -1 6 11; -1 1 3 2 7 -1 -2; 4 3 1 -7 2 1 1; 2 9 -8 11 -1 -4 -1; 7 2 -1 2 7 -1 9;%系數(shù)矩陣b=11 2 29 9 5 8 25;%n維向量y=inv(A)*b %matlab的計(jì)算結(jié)果n=length(b);%方程個(gè)數(shù)nx=zeros(n,1);%未知向量%-消去-for k=1:n-1 Auk=A(k:n,k); m,u=max(abs(Auk); u=u+k-1

4、%u為最大元所在的列 %-交換最大的行和當(dāng)前行的值- for j=k:n temp=A(u,j);A(u,j)=A(k,j);A(k,j)=temp; end temp=b(k);b(k)=b(u);b(u)=temp;% if A(k,k)=0;% error(Error);% end for i=k+1:n% A(i,k)=A(i,k)/A(k,k); Aik=A(i,k)/A(k,k) for j=k:n A(i,j)=A(i,j)-Aik*A(k,j); end A b(i)=b(i)-Aik*b(k) endend %-回代-x(n)=b(n)/A(n,n)for k=n-1:-1:1 S=b(k); for j=k+1:n S=S-A(k,j)*x(j); end x(k