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Monte Carlo solvers of large linear systems with Toeplitz matrices, preconditioning, iterative refinement with applications to integral equations and acoustic inverse problem

  • Karl K. Sabelfeld ORCID logo EMAIL logo and Igor Shafigulin
Published/Copyright: May 22, 2025

Abstract

This study deals with randomized algorithms and random projection methods for solving systems of linear algebraic equations with Toeplitz matrices. A preconditioning of such systems with circulant matrices is used that improves the convergence of the stochastic projection method. The developed stochastic algorithms are applied to first kind boundary integral equations for the Laplace, screened Poisson, and Helmholtz equations. Another application concerns the inverse problem for a wave equation where the task is to recover the unknown coefficient of this equation. A series of computer simulations are carried out to analyze the efficiency of the developed algorithm.

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: 2025-01-03
Revised: 2025-04-18
Accepted: 2025-04-20
Published Online: 2025-05-22
Published in Print: 2025-09-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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