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The Importance of Structure in Incomplete Factorization Preconditioners

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    0351679 - ÚI 2012 RIV SE eng J - Journal Article
    Scott, J. - Tůma, Miroslav
    The Importance of Structure in Incomplete Factorization Preconditioners.
    Bit. Roč. 51, č. 2 (2011), s. 385-404. ISSN 0006-3835
    Grant - others:GA AV ČR(CZ) M100300902
    Institutional research plan: CEZ:AV0Z10300504
    Keywords : sparse symmetric linear systems * incomplete factorizations * preconditioners * level-based approach
    Subject RIV: BA - General Mathematics
    Impact factor: 0.724, year: 2011

    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.
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