IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v31y2025i2p145-162n1005.html
   My bibliography  Save this article

Combining randomized and deterministic iterative algorithms for high accuracy solution of large linear systems and boundary integral equations

Author

Listed:
  • Sabelfeld Karl K.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences; and Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia)

  • Agarkov Georgy

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia)

Abstract

This article continues the research on combined stochastic-deterministic iterative algorithms for solving large system of linear algebraic equations we developed in our previous study [K. K. Sabelfeld and G. Agarkov, Randomized vector algorithm with iterative refinement for solving boundary integral equations, Monte Carlo Methods Appl. 30 2024, 4, 375–388]. In this paper we focus on two issues: Variance reduction and extension of randomized algorithms by combining them with Krylov type iterative methods like the method of conjugate gradients, the conjugate residual method, and Craig’s method. The developed randomized algorithms are applied to boundary integral equations for 2D and 3D Laplace equations.

Suggested Citation

  • Sabelfeld Karl K. & Agarkov Georgy, 2025. "Combining randomized and deterministic iterative algorithms for high accuracy solution of large linear systems and boundary integral equations," Monte Carlo Methods and Applications, De Gruyter, vol. 31(2), pages 145-162.
    • Handle: RePEc:bpj:mcmeap:v:31:y:2025:i:2:p:145-162:n:1005
    DOI: 10.1515/mcma-2025-2008
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2025-2008
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma-2025-2008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:bpj:mcmeap:v:31:y:2025:i:2:p:145-162:n:1005. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.