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

Citer ceci

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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",
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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

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AU - Tshimanga Ilunga, Jean

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KW - preconditioners

KW - limited memory

KW - linear systems

KW - conjugate gradient

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JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

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