I have this code for the Gauss-Seidel iteraton method, but I do not understand what it is computing. Could anyone please explain this code?

%% set random pos def matrix A with large diagonal entry randn('seed', 1); n=50; B=randn(n, n); [Q, R]=qr(B); A=0.5*n*eye(n)+R'*R;

%% set rhs b corresponding to y as the solution y=1:n; y=y(:); b=A*y;

%% attempt to get solution using gauss seidel method x=zeros(n, 1); itmax=100*n; tol=1e-8; done=0; for it=1:itmax

xold=x;
for i=1:n
  t=x;
  t(i)=0;
  x(i)=(b(i)-A(i, :)*t)/A(i,i);
end
er=norm(x-xold);
fprintf('%5d  er=%12.4e\n', it, er);
if er<tol
  fprintf('..now less than %e\n', tol);
  done=1;
  break;
end

end

if done==0 fprintf('..failed to converge with itmax=%d, tol=%e\n', itmax, tol); else fprintf('y, x, y-x follows\n'); [y, x, y-x] end

[Alberto]

Gauss Seidel is an iterative method to solve a system of linear equations. It doesn't converges in every system, it doesnt matter if it has solution or not. The coefficient matrix should be diagonally dominant.