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

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

Journal

Monte Carlo Methods and Applications
ISSN: 0929-9629 , E-ISSN: 1569-3961

Output data

Year: 2025, Volume: 31, Number: 3, Pages: 207-224 Pages count : 18 DOI: 10.1515/mcma-2025-2012

Tags

Toeplitz matrices; circulant preconditioner; Laplace and screened Poisson equations; boundary integral equations; iterative refinement; first kind integral equations; inverse acoustic problem

Authors

Sabelfeld Karl K. ^1,2 , Shafigulin Igor ^1,3

Affiliations

1	Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences ;
2	Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia
3	Novosibirsk State University , Novosibirsk , Russia

Funding (1)

Russian Science Foundation

24-11-00107

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.

Sabelfeld K.K. , Shafigulin I.
Monte Carlo solvers of large linear systems with Toeplitz matrices, preconditioning, iterative refinement with applications to integral equations and acoustic inverse problem
Monte Carlo Methods and Applications. 2025. V.31. N3. P.207-224. DOI: 10.1515/mcma-2025-2012 WOS Scopus OpenAlex

Submitted:	Jan 3, 2025
Accepted:	Apr 20, 2025
Published online:	May 22, 2025
Published print:	Sep 1, 2025

Web of science:	WOS:001494817900001
Scopus:	2-s2.0-105006738145
OpenAlex:	W4410555868

Пока нет цитирований