m-Step preconditioned conjugate gradient methods

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. E...

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Veröffentlicht in:	SIAM journal on scientific and statistical computing 1985-04, Vol.6 (2), p.452-463
1. Verfasser:	ADAMS, L
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Eigenvalues Exact sciences and technology Iterative methods Linear equations Logic and foundations Mathematical logic, foundations, set theory Mathematics Methods Proof theory and constructive mathematics Research centers Sciences and techniques of general use
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Zusammenfassung:	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.
ISSN:	0196-5204 1064-8275 2168-3417 1095-7197
DOI:	10.1137/0906032