Gauss-Seidel Method in Matlab

function [x,info,relres] = myGaussSeidel(A,b,MaxIter,TOL)

%Gaussseidel Method

n=2;

x0=zeros(n,1);

x=zeros(n,1);

k=1;

relres=0;

while k<=MaxIter

for i=1:n

x(i)=(b(i)-A(i,1:i-1)*x(1:i-1)-A(i,i-1:n)*x0(i+1:n))/A(i,i); % HOW TO DISTINGUISH UPDATED AND UNUPDATED TERMS OF X?

x0=x;

if norm(A*x-b)/norm(b)<=TOL

disp(x);

info=info+1;

end

end

info=-1;

k=k+1;

end

disp(x);

end

This code is my implementation for Gauss-Seidel Method, In line "x(i)=(b(i)-A(i,1:i-1)*x(1:i-1)-A(i,i-1:n)*x0(i+1:n))/A(i,i); " How to show the updated and unupdated values? I do not think my current code gives the correct answer.

Answer 1

[Pavan Guntha]

Hi Zhukun,

You could use another vector y to store the values in the vector x and compare the updated x vector to the vector y in each iteration to determine the updated and unupdated values. This idea is illustrated below:

while k<=MaxIter
    y = x; % y contains the values of vector x which were updated in the previous iteration.
    for i=1:n
        x(i)=(b(i)-A(i,1:i-1)*x(1:i-1)-A(i,i-1:n)*x0(i+1:n))/A(i,i);
        x0=x; 
        if norm(A*x-b)/norm(b)<=TOL   
            disp(x);
            info=info+1;
        end
    end
    % At this point, x contains the values updated in the current iteration whereas y
    % has the values updated in the previous iteration.
    info=-1;
    k=k+1;
end

You can also have a look at a similar case: Link

Hope this helps!