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A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices

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    0404726 - UIVT-O 20030114 RIV GB eng J - Journal Article
    Benzi, M. - Tůma, Miroslav
    A Robust Incomplete Factorization Preconditioner for Positive Definite Matrices.
    Numerical Linear Algebra with Applications. Roč. 10, - (2003), s. 385-400. ISSN 1070-5325
    R&D Projects: GA AV ČR IAA2030801; GA AV ČR IAA1030103
    Institutional research plan: AV0Z1030915
    Keywords : sparse linear systems * positive definite matrices * preconditioned conjugate gradients * incomplete factorization * A-orthogonalization * SAINV
    Subject RIV: BA - General Mathematics
    Impact factor: 1.042, year: 2003

    We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive definite matrix A. The factorization is not based on the Cholesky algorithm 9or Gaussian elimination0, but on A-orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modification. When used in conjunction with the conjugate gradient algorithin, the new preconditioner results in a reliable solver for highly ill-conditioned linear systems. Comparisons with other incomplete factorization techniques using challenging linear systems from structural analysis and solid mechanics problems are presented.
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