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Notes on a 3-term Conjugacy Recurrence for the Iterative Solution of Symmetric Linear Systems

Author

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  • Giovanni Fasano

    (Department of Applied Mathematics, University of Venice)

Abstract

We consider a 3-term recurrence, namely CG_2step, for the iterative solution of symmetric linear systems. The new algorithm generates conjugate directions and extends some standard theoretical properties of the Conjugate Gradient (CG) method [10]. We prove the finite convergence of CG_2step, and we provide some error analysis. Then, we introduce preconditioning for CG_2step, and we prove that standard error bounds for the CG also hold for our proposal.

Suggested Citation

  • Giovanni Fasano, 2008. "Notes on a 3-term Conjugacy Recurrence for the Iterative Solution of Symmetric Linear Systems," Working Papers 179, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    • Handle: RePEc:vnm:wpaper:179
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    File URL: http://virgo.unive.it/wpideas/storage/2008wp179.pdf
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    References listed on IDEAS

    as
    1. G. Fasano, 2007. "Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 267-285, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Iterative methods; 3-term recurrences; Conjugate Gradient method; Error Analysis; Preconditioning;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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