SOLE :: Successive over-relaxation

function [x] = successive_over_relaxation(A, b, x_1, max_error, max_iter, omega)

    [rows, cols] = size(A);

    if rows ~= cols
        return;
    end

    x = x_1;
    for counter = 1: max_iter
        for i = 1:rows
            sum = 0;
            for j = 1:i-1
                sum = sum + x(j)*A(i, j);
            end

            for j = i+1:cols
                sum = sum + x_1(j)*A(i, j);
            end
            x(i) = (1 - omega)*x_1(i) + omega*(b(i) - sum)/A(i, i);
        end

        if abs(x-x_1) < max_error
            break
        end

        x_1 = x;
    end
end