gauss_seidel.m

给出了线性方程组的CG法、Gauss_Seidel、SOR、Jacobi、fem求解

clear all
clc

format long

% A=[10 -1 2 0;-1 11 -1 3;2 -1 10 -1;0 3 -1 8];
% b=[6;25;-11;5];

A=[10 3 1;2 -10 3;1 3 10];
b=[14;-5;14];
x=zeros(size(b));
y=zeros(size(b));
n=length(b);

zhenjie=inv(A)*b;
k=0;
jingdu=1;
% while jingdu>1e-6
while k<=4
    k=k+1;
    for i=1:n
        if i==1
            y(i)=(b(i)-A(i,i+1:n)*x(i+1:n))/A(i,i);
        elseif i>=2 & i<=n-1
            y(i)=(b(i)-A(i,1:i-1)*y(1:i-1)-A(i,i+1:n)*x(i+1:n))/A(i,i);
        else
            y(i)=(b(i)-A(i,1:i-1)*y(1:i-1))/A(i,i);
        end
    end
    jingdu=norm(zhenjie-y,2);
   x=y;
end
x