Gauss-Seidel iterative method algorithm in Matlab

Gauss-Seidel iterative method algorithm in Matlab :

function gauss_seidel(A, b, N) %Gauss_seidel(A, b, N) solve iteratively a system of linear equations %whereby A is the coefficient matrix, and b is the right-hand side column vector. %N is the maximum number of iterations. %The method implemented is the Gauss-Seidel iterative. %The starting vector is the null vector, but can be adjusted to one's needs. %The iterative form is based on the Gauss-Seidel transition/iteration matrix %Tg = inv(D-L)*U and the constant vector cg = inv(D-L)*b. %The output is the solution vector x. %This file follows the algorithmic guidelines given in the book %Numerical Analysis, 7th Ed, by Burden & Faires %Author: Alain G. Kapitho %Date : Dec. 2005 %Rev. : Aug. 2007 n = size(A,1); %splitting matrix A into the three matrices L, U and D D = diag(diag(A)); L = tril(-A,-1); U = triu(-A,1); %transition matrix and constant vector used for iterations Tg = inv(D-L)*U; cg = inv(D-L)*b; tol = 1e-05; k = 1; x = zeros(n,1); %starting vector while k <= N x(:,k+1) = Tg*x(:,k) + cg; if norm(x(:,k+1)-x(:,k)) < tol disp('The procedure was successful') disp('Condition ||x^(k+1) - x^(k)|| < tol was met after k iterations') disp(k); disp('x = ');disp(x(:,k+1)); break end k = k+1; end if norm(x(:,k+1)- x(:,k)) > tol || k > N disp('Maximum number of iterations reached without satisfying condition:') disp('||x^(k+1) - x^(k)|| < tol'); disp(tol); disp('Please, examine the sequence of iterates') disp('In case you observe convergence, then increase the maximum number of iterations') disp('In case of divergence, the matrix may not be diagonally dominant') disp(x'); end