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

  • Karl K. Sabelfeld ORCID logo EMAIL logo und Georgy Agarkov
Veröffentlicht/Copyright: 28. März 2025

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.

MSC 2020: 65C05; 65C40; 65Z05

Award Identifier / Grant number: 24-11-00107

Funding statement: Support by the Russian Science Foundation under Grant 24-11-00107 is greatly acknowledged.

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Received: 2024-12-31
Revised: 2025-03-14
Accepted: 2025-03-16
Published Online: 2025-03-28
Published in Print: 2025-06-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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