The Importance of Structure in Incomplete Factorization Preconditioners

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F11%3A00351679" target="_blank" >RIV/67985807:_____/11:00351679 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10543-010-0299-8" target="_blank" >http://dx.doi.org/10.1007/s10543-010-0299-8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10543-010-0299-8" target="_blank" >10.1007/s10543-010-0299-8</a>

Result language
angličtina
Original language name
The Importance of Structure in Incomplete Factorization Preconditioners
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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