Algorithme d'Itération de Gauss–Seidel en Matlab

Algorithme d'Itération de Gauss–Seidel en Matlab :

function X = gauseid(A,B,X0,kmax) %This function finds x = A^-1 B by Gauss–Seidel iteration. if nargin < 4, tol = 1e-6; kmax = 100; elseif kmax < 1, tol = max(kmax,1e-16); kmax = 1000; else tol = 1e-6; end if nargin < 4, tol = 1e-6; kmax = 100; end if nargin < 3, X0 = zeros(size(B)); end NA = size(A,1); X = X0; for k = 1: kmax X(1,:) = (B(1,:)-A(1,2:NA)*X(2:NA,:))/A(1,1); for m = 2:NA-1 tmp = B(m,:)-A(m,1:m-1)*X(1:m - 1,:)-A(m,m + 1:NA)*X(m + 1:NA,:); X(m,:) = tmp/A(m,m); %Eq.(2.5.4) end X(NA,:) = (B(NA,:)-A(NA,1:NA - 1)*X(1:NA - 1,:))/A(NA,NA); if nargout == 0, X, end %To see the intermediate results if norm(X - X0)/(norm(X0) + eps)<tol, break; end X0 = X; end