Overlapping additive and multiplicative Schwarz iterations for H -matrices

Abstract

In recent years, an algebraic framework was introduced for the analysis of convergence of Schwarz methods for the solution of linear systems of the form Ax=b. Within this framework, additive and multiplicative Schwarz were shown to converge when the coefficient matrix A is a nonsingular M-matrix, or a symmetric positive definite matrix. In this paper, many of these results are extended to the case of A being an H-matrix. The case of inexact local solves is also considered. In addition, the two-level scheme is studied, i.e., when a coarse grid correction is used in conjunction with the additive or the multiplicative Schwarz iterations. © 2003 Elsevier Inc. All rights reserved.