Block two-stage preconditioners

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Abstract

Linear systems of the form Ax = b, where the matrix A is symmetric and positive definite, often arise from the discretization of elliptic partial differential equations. A very successful method for solving these linear systems is the preconditioned conjugate gradient method. In this paper, we study parallel preconditioners for the conjugate gradient method based on the block two-stage iterative methods. Sufficient conditions for the validity of these preconditioners are given. Computational results of these preconditioned conjugate gradient methods on two parallel computing systems are presented.

Keywords

Linear systems
Symmetric matrices
Positive definite matrices
Iterative methods
Block methods
Two-stage methods
Preconditioned conjugate gradient method

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This research was supported by Spanish DGESIC Grant Number PB98-0977.

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〈chus〉〈violeta〉〈jpenades〉@dccia.ua.es