On the Dynamic Acceleration of the Preconditioned Simultaneous Displacement (PSD) Method

Abstract

The Preconditioned Simultaneous Displacement (PSD) iterative method is considered for the solution of symmetric, sparse matrix problems. The development of a dynamic algorithm for improving the estimates of the involved parameters is presented. These estimates are then used to accelerate the PSD method by employing semi-iterative techniques. The algorithm determines adaptively a sequence of parameters while the iteration is in progress without requiring preliminary eigenvalue estimates (only trivial input parameters are required). The performance of the algorithm is tested on a number of generalised Dirichlet problems. It is seen that the attained rate of convergence is approximately Q(h1/2) and is better than the algorithm using estimated parameters in certain cases. © 1981, Taylor & Francis Group, LLC. All rights reserved