IDEAS home Printed from https://ideas.repec.org/p/vnm/wpaper/179.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://virgo.unive.it/wpideas/storage/2008wp179.pdf
    File Function: First version, 2008
    Download Restriction: no
    ---><---

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giovanni Fasano, 2015. "A Framework of Conjugate Direction Methods for Symmetric Linear Systems in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 883-914, March.
    2. Renato De Leone & Giovanni Fasano & Yaroslav D. Sergeyev, 2018. "Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming," Computational Optimization and Applications, Springer, vol. 71(1), pages 73-93, September.
    3. Giovanni Fasano & Massimo Roma, 2013. "Preconditioning Newton–Krylov methods in nonconvex large scale optimization," Computational Optimization and Applications, Springer, vol. 56(2), pages 253-290, October.
    4. 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.
    5. Andrea Caliciotti & Giovanni Fasano & Florian Potra & Massimo Roma, 2020. "Issues on the use of a modified Bunch and Kaufman decomposition for large scale Newton’s equation," Computational Optimization and Applications, Springer, vol. 77(3), pages 627-651, December.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vnm:wpaper:179. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Daria Arkhipova (email available below). General contact details of provider: https://edirc.repec.org/data/dmvenit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.