ljacobi.m

jaccobi迭代法和GS迭代法求解线性方程组

%Jacobi 迭代法解线性方程组
%AX=b，A=D-L-U
%X=D'(L+U)X+D'b=BX+f
function [x,e]=ljacobi(n,A,b,N,x0)
a=A;x0=x0';x(n)=0;
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,i)=a(i,i);
end
%L=D-A;B=inv(D)*L;f=inv(D)*b';
for k=1:(N-1)
    for i=1:n
        s=0;
        for j=1:n
            s=s+a(i,j)*x0(j);
        end
        s=s-a(i,i)*x0(i);
        x(i)=(b(i)-s)/a(i,i);
    end
    x0=x;
end
for i=1:n
    s=0;
    for j=1:n
        s=s+a(i,j)*x0(j);
    end
    s=s-a(i,i)*x0(i);
    x(i)=(b(i)-s)/a(i,i);
end
e=sum(abs(x-x0));