Block two-stage preconditioners

Linear systems of the form Ax = b, where the matrix A is symmetric and posi tive definite, often arise from the discretization of elliptic partial diff erential Equations. A very successful method for solving these linear syste ms is the preconditioned conjugate gradient method. In this paper, we study parallel preconditioners for the conjugate gradient method based on the bl ock two-stage iterative methods. Sufficient conditions for the validity of these preconditioners are given. Computational results of these preconditio ned conjugate gradient methods on two parallel computing systems are presen ted. (C) 2001 Elsevier Science Ltd. All rights reserved.