solve a system of equations using gauss-seirdel interation in matlab

main.m
% A is the coefficient matrix of the system of linear equations
A = [4 -1 0; 1 5 -2; 0 -2 4];

% b is the constant vector of the system of linear equations
b = [21; -8; 20];

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

% Maximum number of iterations
maxIter = 100;

% Tolerance for the solution
tol = 1e-6;

% Dimension of the system
n = length(b);

% Preallocate memory for the solution
x = zeros(n, 1);

% Gauss-Seidel iteration
for k = 1: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);
    end
    if norm(x - x0) < tol % Check for convergence
        break;
    end
    x0 = x; % Update the solution
end

% The solution is the vector x
x
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