%GS(Gauss-Seidel)迭代法解線性方程組
%AX=b，A=D-L-U
%X=inv(D-L)UX+inv(D-L)b=GX+f
function [x,e,G]=lgs(n,A,b,N,x0)
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
    D(i,1:i)=a(i,1:i);
end
U=D-A;G=inv(D)*U;f=inv(D)*b';
for k=1:(N-1)
    x=G*x0+f;
    x0=x;
end
x=G*x0+f;
e=sum(abs(x-x0));