gaussseidel in matlab

main.m
% Initialize the matrix A and vector b
A = [4,-1,0; -1,4,-1; 0,-1,3];
b = [12; 15; 10];

% Set the initial guess for solution
x0 = [0; 0; 0];

% Set the tolerance and maximum number of iterations
tol = 1e-6;  % relative error tolerance
maxit = 100; % maximum number of iterations

% Initialize the solution vector and the iteration counter
x = x0;
iter = 0;

% Gauss Seidel iteration loop
while(iter < maxit)
    xold = x;
    for i = 1:length(x)
        sigma = 0;
        for j = 1:length(x)
            if (j ~= i)
                sigma = sigma + A(i,j)*x(j);
            end
        end
        x(i) = (1/A(i,i))*(b(i) - sigma);
    end
    % Check for convergence
    if (norm(x-xold)/norm(xold) < tol)
        break;
    end
    iter = iter+1;
end

% print the result
fprintf('The solution is: x = %f, %f, %f\n', x(1), x(2), x(3));
fprintf('Number of iterations = %d\n', iter);
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