The CG-algorithm is an iterative method to solve linear systems $$Ax + b = 0$$ (1) where A is a symmetric and positive definite coefficient matrix of order n. The method has been described first by Stiefel and Hesteness [1, 2] and additional information is contained in [3] and [4]. The notations used here coincide partially with those used in [5] where also the connexions with other methods and generalisations of the CG-algorithm are presented.