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1985•SIAM Journal on Scientific and Statistical ComputingRequires access

m -Step Preconditioned Conjugate Gradient Methods

Loyce M. Adams

Open publisher page 89 citations

Abstract

This paper discusses preconditioners for the conjugate gradient method which are based on several iterations of stationary iterative methods. Necessary and sufficient conditions are given for the applicability of these preconditioners to symmetric and positive definite systems of linear equations. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

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What this paper is about

This paper discusses preconditioners for the conjugate gradient method which are based on several iterations of stationary iterative methods. Necessary and sufficient conditions are given for the applicability of these preconditioners to symmetric and positive definite systems of linear equations. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

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OpenAlex reports 89 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper discusses preconditioners for the conjugate gradient method which are based on several iterations of stationary iterative methods. Necessary and sufficient conditions are given for the applicability of these preconditioners to symmetric and positive definite systems of linear equations. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

Key concepts: Conjugate gradient method, Conjugate residual method, Derivation of the conjugate gradient method, Linear system, Conjugate, Applied mathematics, Finite element method, Mathematics

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