On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

This work studies a class of limited memory preconditioners (LMPs) for solving linear (positive-definite) systems of equations with multiple right-hand sides. We propose a class of (LMPs), whose construction requires a small number of linearly independent vectors. After exploring the theoretical properties of the preconditioners, we focus on three particular members: spectral-LMP, quasi-Newton-LMP, and Ritz-LMP. We show that the first two are well known, while the third is new. Numerical tests indicate that the Ritz-LMP is efficient on a real-life nonlinear optimization problem arising in a data assimilation system for oceanography.
langue originaleAnglais
Pages (de - à)912-935
Nombre de pages24
journalSIAM Journal on Optimization
Numéro de publication3
étatNon publié - 2011

Empreinte digitale

Large-scale Systems
Preconditioner
Linear systems
Linear Systems
Data storage equipment
Oceanography
Quasi-Newton
Data Assimilation
Nonlinear Optimization
Class
Positive definite
System of equations
Nonlinear Problem
Linearly
Optimization Problem

mots-clés

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    title = "On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides",
    abstract = "This work studies a class of limited memory preconditioners (LMPs) for solving linear (positive-definite) systems of equations with multiple right-hand sides. We propose a class of (LMPs), whose construction requires a small number of linearly independent vectors. After exploring the theoretical properties of the preconditioners, we focus on three particular members: spectral-LMP, quasi-Newton-LMP, and Ritz-LMP. We show that the first two are well known, while the third is new. Numerical tests indicate that the Ritz-LMP is efficient on a real-life nonlinear optimization problem arising in a data assimilation system for oceanography.",
    keywords = "preconditioners, limited memory , linear systems, conjugate gradient",
    author = "Serge Gratton and Annick Sartenaer and {Tshimanga Ilunga}, Jean",
    year = "2011",
    language = "English",
    pages = "912--935",
    journal = "SIAM Journal on Optimization",
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    On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides. / Gratton, Serge; Sartenaer, Annick; Tshimanga Ilunga, Jean.

    Dans: SIAM Journal on Optimization, Numéro 3, 2011, p. 912-935.

    Résultats de recherche: Contribution à un journal/une revueArticle

    TY - JOUR

    T1 - On a class of limited memory preconditioners for large scale linear systems with multiple right-hand sides

    AU - Gratton, Serge

    AU - Sartenaer, Annick

    AU - Tshimanga Ilunga, Jean

    PY - 2011

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    AB - This work studies a class of limited memory preconditioners (LMPs) for solving linear (positive-definite) systems of equations with multiple right-hand sides. We propose a class of (LMPs), whose construction requires a small number of linearly independent vectors. After exploring the theoretical properties of the preconditioners, we focus on three particular members: spectral-LMP, quasi-Newton-LMP, and Ritz-LMP. We show that the first two are well known, while the third is new. Numerical tests indicate that the Ritz-LMP is efficient on a real-life nonlinear optimization problem arising in a data assimilation system for oceanography.

    KW - preconditioners

    KW - limited memory

    KW - linear systems

    KW - conjugate gradient

    M3 - Article

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    EP - 935

    JO - SIAM Journal on Optimization

    JF - SIAM Journal on Optimization

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