The Gauss-Seidel method implemented in Octave.

gauss_seidel.m

function xnew = gauss_seidel(A, b, xold)
  % This implementation of the Gauss-Seidel method in Octave uses
  % a single loop.  It is based on the solution provided in the 
  % APM1513 course work from UNISA.

  % We first need to determine how many equations we need to solve
  n = size(A, 1);
  % We set the xnew to have the xold values
  xnew = xold;
  
  % Loop through each equation and determine a new x value for the 
  % xnew vector
  for k = 1:n
    % We first get the number in the diagonal for the current row in
    % the matrix
    diagonal_value = A(k,k);
    
    % We then set that diagonal to 0 so that it will not affect our 
    % calculation of the x value in the next step
    A(k,k) = 0;
    
    % We then calculate the xnew value for the equation
    xnew(k) = (b(k) - A(k,:)*xnew) / diagonal_value;
  endfor
endfunction

Hello there may i ask which version of Octave is the above code written in, i'm guessing it's the latest 6.2.0?