The Aitken's -prediction of C. Brezinski and M. Redivo Zaglia has already been used by M. Morandi Cecchi, M. Redivo Zaglia and G. Scenna in order to compute a numerical approximation of the solution of a parabolic initial-boundary value problem. This method consists in two consecutive steps: the first one is the approximation with a finite elements method, where the solution of the involved nonlinear system is computed by Gauss–Seidel method; the second one is a prediction of further terms with Aitken's -process. By comparison with this method, we use other methods of prediction in another way. First, we consider a generalization of -prediction. In this paper, we only use vector prediction which is more stable than the scalar one. Then, the methods of prediction presented can be used in order to predict the starting vector of the Gauss–Seidel method.