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The Importance of Structure in Incomplete Factorization Preconditioners
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SYSNO ASEP 0351679 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Importance of Structure in Incomplete Factorization Preconditioners Author(s) Scott, J. (GB)
Tůma, Miroslav (UIVT-O) SAI, RID, ORCIDSource Title Bit. - : Springer - ISSN 0006-3835
Roč. 51, č. 2 (2011), s. 385-404Number of pages 20 s. Language eng - English Country SE - Sweden Keywords sparse symmetric linear systems ; incomplete factorizations ; preconditioners ; level-based approach Subject RIV BA - General Mathematics CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000291482000008 EID SCOPUS 79958190216 DOI 10.1007/s10543-010-0299-8 Annotation In this paper, we consider level-based preconditioning, which is one of the basic approaches to incomplete factorization preconditioning of iterative methods. It is well-known that while structure-based preconditioners can be very useful, excessive memory demands can limit their usefulness. Here we present an improved strategy that considers the individual entries of the system matrix and restricts small entries to contributing to fewer levels of fill than the largest entries. Using symmetric positive-definite problems arising from a wide range of practical applications, we show that the use of variable levels of fill can yield incomplete Cholesky factorization preconditioners that are more efficient than those resulting from the standard level-based approach. Further numerical results demonstrate that our level-based approach can lead to much sparser but efficient incomplete factorization preconditioners. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2012
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