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Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems

SYSNO ASEP	0086650
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Efficient Preconditioning of Sequences of Nonsymmetric Linear Systems
Title	Efektivní předpodmínění posloupností nesymetrických lineárních systémů
Author(s)	Duintjer Tebbens, Jurjen (UIVT-O)_{RID, SAI, ORCID} Tůma, Miroslav (UIVT-O)_{SAI, RID, ORCID}
Source Title	SIAM Journal on Scientific Computing. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1064-8275 Roč. 29, č. 5 (2007), s. 1918-1941
Number of pages	24 s.
Language	eng - English
Country	US - United States
Keywords	preconditioned iterative methods ; sparse matrices ; sequences of linear algebraic systems ; incomplete factorizations ; factorization updates ; Gauss–Jordan transformations ; minimum spanning tree
Subject RIV	BA - General Mathematics
R&D Projects	1ET400300415 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
	KJB100300703 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR)
CEZ	AV0Z10300504 - UIVT-O (2005-2011)
UT WOS	000250005700006
EID SCOPUS	52149094645
DOI	10.1137/06066151X
Annotation	We present a new approach for approximate updates of factorized nonsymmetric preconditioners for solving sequences of linear algebraic systems. This approach is algebraic and it is theoretically motivated. It generalizes diagonal updates introduced by Benzi and Bertaccini [BIT, 43 (2003), pp. 231–244] and Bertaccini [Electron. Trans. Numer. Anal., 18 (2004), pp. 49–64]. It is successful in significantly decreasing the number of iterations of a preconditioned iterative method for solving subsequent systems of a sequence when compared with freezing the preconditioner from the first system of the sequence. In some cases, the updated preconditioners offer a rate of convergence similar to or even higher than the rate obtained when preconditioning with recomputed preconditioners. Since the updates are typically cheap and straightforward, their use is of practical interest.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2008

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