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

Author

Listed:
  • Giovanni Fasano

    (Department of Management, Università Ca' Foscari Venezia)

  • Massimo Roma

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

Abstract

In this paper we consider the parameter dependent class of preconditioners M(a,d,D) defined in the companion paper The latter was constructed by using information from a Krylov subspace method, adopted to solve the large symmetric linear system Ax = b. We first estimate the condition number of the preconditioned matrix M(a,d,D). Then our preconditioners, which are independent of the choice of the Krylov subspace method adopted, proved to be effective also when solving sequences of slowly changing linear systems, in unconstrained optimization and linear algebra frameworks. A numerical experience is provided to give evidence of the performance of M(a,d,D).

Suggested Citation

  • 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 5, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    • Handle: RePEc:vnm:wpdman:5
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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 5, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    2. Renato Leone & Giovanni Fasano & Massimo Roma & Yaroslav D. Sergeyev, 2020. "Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 554-589, August.
    3. G. Fasano, 2005. "Planar Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization, Part 1: Theory," Journal of Optimization Theory and Applications, Springer, vol. 125(3), pages 523-541, June.
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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 5, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.

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    More about this item

    Keywords

    preconditioners; large indefinite linear systems; large scale nonconvex optimization; Krylov subspace methods;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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