Standard

Monte Carlo solvers of large linear systems with Toeplitz matrices, preconditioning, iterative refinement with applications to integral equations and acoustic inverse problem. / Sabelfeld, Karl K.; Shafigulin, Igor.

в: Monte Carlo Methods and Applications, 22.05.2025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Sabelfeld, KK & Shafigulin, I 2025, '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. https://doi.org/10.1515/mcma-2025-2012

APA

Sabelfeld, K. K., & Shafigulin, I. (2025). 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. https://doi.org/10.1515/mcma-2025-2012

Vancouver

Sabelfeld KK, 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 май 22. doi: 10.1515/mcma-2025-2012

Author

Sabelfeld, Karl K. ; Shafigulin, Igor. / Monte Carlo solvers of large linear systems with Toeplitz matrices, preconditioning, iterative refinement with applications to integral equations and acoustic inverse problem. в: Monte Carlo Methods and Applications. 2025.

BibTeX

@article{623dead8d08d41b58649c16bb2cb765b,
title = "Monte Carlo solvers of large linear systems with Toeplitz matrices, preconditioning, iterative refinement with applications to integral equations and acoustic inverse problem",
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.",
keywords = "Laplace and screened Poisson equations, Toeplitz matrices, boundary integral equations, circulant preconditioner, first kind integral equations, inverse acoustic problem, iterative refinement",
author = "Sabelfeld, {Karl K.} and Igor Shafigulin",
note = "Funding statement: Support by the Russian Science Foundation under Grant 24-11-00107 is greatly acknowledged.",
year = "2025",
month = may,
day = "22",
doi = "10.1515/mcma-2025-2012",
language = "English",
journal = "Monte Carlo Methods and Applications",
issn = "0929-9629",
publisher = "Walter de Gruyter GmbH",

}

RIS

TY - JOUR

T1 - Monte Carlo solvers of large linear systems with Toeplitz matrices, preconditioning, iterative refinement with applications to integral equations and acoustic inverse problem

AU - Sabelfeld, Karl K.

AU - Shafigulin, Igor

N1 - Funding statement: Support by the Russian Science Foundation under Grant 24-11-00107 is greatly acknowledged.

PY - 2025/5/22

Y1 - 2025/5/22

N2 - 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.

AB - 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.

KW - Laplace and screened Poisson equations

KW - Toeplitz matrices

KW - boundary integral equations

KW - circulant preconditioner

KW - first kind integral equations

KW - inverse acoustic problem

KW - iterative refinement

UR - https://www.mendeley.com/catalogue/b33fdbf7-65c8-3a0e-973b-61bd6026a5e8/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105006738145&origin=inward&txGid=8249db0896aacdd0c11c0575715712c0

U2 - 10.1515/mcma-2025-2012

DO - 10.1515/mcma-2025-2012

M3 - Article

JO - Monte Carlo Methods and Applications

JF - Monte Carlo Methods and Applications

SN - 0929-9629

ER -

ID: 67454841