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

Serge Gratton, Annick Sartenaer, Jean Tshimanga Ilunga

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)912-935
Number of pages24
JournalSIAM Journal on Optimization
Issue number3
Publication statusUnpublished - 2011

Keywords

  • preconditioners
  • limited memory
  • linear systems
  • conjugate gradient

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