Richardson method and totally nonnegative linear systems

We show that modified Richardson method converges for any nonsingular totally nonnegative stochastic matrix for any choice of the parameter between 0 and 2. We present a variant of the modified Richardson method that is convergent for any nonsingular totally nonnegative matrix. We obtain the optimal parameter value for this method and give a procedure for estimating it. Numerical experiments are presented. (C) 2010 Elsevier Inc. All rights reserved.