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A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part I

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  • Giovanni Fasano

    ()
    (Department of Management, Università Ca' Foscari Venezia)

  • Massimo Roma

    ()
    (Dipartimento di Informatica e Sistemistica "A. Ruberti", Università Sapienza Roma)

Abstract

We propose a class of preconditioners, which are also tailored for symmetric linear systems from linear algebra and nonconvex optimization. Our preconditioners are specifically suited for large linear systems and may be obtained as by-product of Krylov subspace solvers. Each preconditioner in our class is identified by setting the values of a pair of parameters and a scaling matrix, which are user-dependent, and may be chosen according with the structure of the problem in hand. We provide theoretical properties for our preconditioners. In particular, we show that our preconditioners both shift some eigenvalues of the system matrix to controlled values, and they tend to reduce the modulus of most of the other eigenvalues. In a companion paper we study some structural properties of our class of preconditioners, and report the results on a significant numerical experience.

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File URL: http://virgo.unive.it/wpideas/storage/2011wp4.pdf
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Bibliographic Info

Paper provided by Department of Management, Università Ca' Foscari Venezia in its series Working Papers with number 4.

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Length: 16 pages
Date of creation: Jun 2011
Date of revision:
Handle: RePEc:vnm:wpdman:4

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Related research

Keywords: preconditioners; large indefinite linear systems; large scale nonconvex optimization; Krylov subspace methods;

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  1. Giovanni Fasano & Massimo Roma, 2011. "A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part II," Working Papers, Department of Management, Università Ca' Foscari Venezia 5, Department of Management, Università Ca' Foscari Venezia.
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Cited by:
  1. Giovanni Fasano & Massimo Roma, 2011. "A Class of Preconditioners for Large Indefinite Linear Systems, as by-product of Krylov subspace Methods: Part II," Working Papers, Department of Management, Università Ca' Foscari Venezia 5, Department of Management, Università Ca' Foscari Venezia.

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