lsor.m

SOR（超松弛）迭代发求解线性方程组问题

%SOR（超松弛）迭代法
%AX=b，A=D-L-U，引入松弛因子w
%X=inv(D-wL)[(1-w)D+wU]X+inv(D-wL)wb=LwX+f
function [x,e,Lw]=lsor(n,A,b,N,x0,w)
a=A;x0=x0';
D=zeros(n);L=zeros(n);U=zeros(n);
for i=1:n
    if a(i,i)==0
        fprintf('the element on the cross is zero!Error!');
        return;
    end
    L(i,1:i)=a(i,1:i);
    D(i,i)=a(i,i);
end
U=L-A;G=inv(L)*U;
L=D-L;
DL=inv(D-w*L);
Lw=DL*((1-w)*D+w*U);
f=w*DL*b';
for k=1:(N-1)
    x=Lw*x0+f;
    x0=x;
end
x=Lw*x0+f;
e=sum(abs(x-x0));