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Parallel combined chebyshev and least squares iterations in the krylov subspaces. / Gurieva, Yana; Il’in, Valery.

Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers. ed. / Leonid Sokolinsky; Mikhail Zymbler. Springer Gabler, 2020. p. 162-177 (Communications in Computer and Information Science; Vol. 1263 CCIS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Gurieva, Y & Il’in, V 2020, Parallel combined chebyshev and least squares iterations in the krylov subspaces. in L Sokolinsky & M Zymbler (eds), Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers. Communications in Computer and Information Science, vol. 1263 CCIS, Springer Gabler, pp. 162-177, 14th International Scientific Conference on Parallel Computational Technologies, PCT 2020, Perm, Russian Federation, 27.05.2020. https://doi.org/10.1007/978-3-030-55326-5_12

APA

Gurieva, Y., & Il’in, V. (2020). Parallel combined chebyshev and least squares iterations in the krylov subspaces. In L. Sokolinsky, & M. Zymbler (Eds.), Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers (pp. 162-177). (Communications in Computer and Information Science; Vol. 1263 CCIS). Springer Gabler. https://doi.org/10.1007/978-3-030-55326-5_12

Vancouver

Gurieva Y, Il’in V. Parallel combined chebyshev and least squares iterations in the krylov subspaces. In Sokolinsky L, Zymbler M, editors, Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers. Springer Gabler. 2020. p. 162-177. (Communications in Computer and Information Science). doi: 10.1007/978-3-030-55326-5_12

Author

Gurieva, Yana ; Il’in, Valery. / Parallel combined chebyshev and least squares iterations in the krylov subspaces. Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers. editor / Leonid Sokolinsky ; Mikhail Zymbler. Springer Gabler, 2020. pp. 162-177 (Communications in Computer and Information Science).

BibTeX

@inproceedings{a889c743df4243aca5f1e59105f1b4c2,
title = "Parallel combined chebyshev and least squares iterations in the krylov subspaces",
abstract = "The combined Chebyshev−Least Squares iterative processes in the Krylov subspaces to solve symmetric and non-symmetric systems of linear algebraic equations (SLAEs) are proposed. This approach is a generalization of the Anderson acceleration of the Jacobi iterative method as an efficient alternative to the Krylov methods. The algorithms proposed are based on constructing some basis of the Krylov subspaces and a minimization of the residual vector norm by means of the least squares procedure. The general process includes periodical restarts and can be considered to be an implicit implementation of the Krylov procedure which can be efficiently parallelized. A comparative analysis of the methods proposed and the classic Krylov approaches is presented. A parallel implementation of the iterative methods on multi-processor computer systems is discussed. The efficiency of the algorithms is demonstrated via the results of numerical experiments on a set of model SLAEs.",
keywords = "Anderson acceleration, Chebyshev iterative algorithms, Convergence of iterations, Krylov subspaces, Least squares, Numerical experiments, Numerical stability",
author = "Yana Gurieva and Valery Il{\textquoteright}in",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.; 14th International Scientific Conference on Parallel Computational Technologies, PCT 2020 ; Conference date: 27-05-2020 Through 29-05-2020",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-55326-5_12",
language = "English",
isbn = "9783030553258",
series = "Communications in Computer and Information Science",
publisher = "Springer Gabler",
pages = "162--177",
editor = "Leonid Sokolinsky and Mikhail Zymbler",
booktitle = "Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers",
address = "Germany",

}

RIS

TY - GEN

T1 - Parallel combined chebyshev and least squares iterations in the krylov subspaces

AU - Gurieva, Yana

AU - Il’in, Valery

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The combined Chebyshev−Least Squares iterative processes in the Krylov subspaces to solve symmetric and non-symmetric systems of linear algebraic equations (SLAEs) are proposed. This approach is a generalization of the Anderson acceleration of the Jacobi iterative method as an efficient alternative to the Krylov methods. The algorithms proposed are based on constructing some basis of the Krylov subspaces and a minimization of the residual vector norm by means of the least squares procedure. The general process includes periodical restarts and can be considered to be an implicit implementation of the Krylov procedure which can be efficiently parallelized. A comparative analysis of the methods proposed and the classic Krylov approaches is presented. A parallel implementation of the iterative methods on multi-processor computer systems is discussed. The efficiency of the algorithms is demonstrated via the results of numerical experiments on a set of model SLAEs.

AB - The combined Chebyshev−Least Squares iterative processes in the Krylov subspaces to solve symmetric and non-symmetric systems of linear algebraic equations (SLAEs) are proposed. This approach is a generalization of the Anderson acceleration of the Jacobi iterative method as an efficient alternative to the Krylov methods. The algorithms proposed are based on constructing some basis of the Krylov subspaces and a minimization of the residual vector norm by means of the least squares procedure. The general process includes periodical restarts and can be considered to be an implicit implementation of the Krylov procedure which can be efficiently parallelized. A comparative analysis of the methods proposed and the classic Krylov approaches is presented. A parallel implementation of the iterative methods on multi-processor computer systems is discussed. The efficiency of the algorithms is demonstrated via the results of numerical experiments on a set of model SLAEs.

KW - Anderson acceleration

KW - Chebyshev iterative algorithms

KW - Convergence of iterations

KW - Krylov subspaces

KW - Least squares

KW - Numerical experiments

KW - Numerical stability

UR - http://www.scopus.com/inward/record.url?scp=85089317012&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-55326-5_12

DO - 10.1007/978-3-030-55326-5_12

M3 - Conference contribution

AN - SCOPUS:85089317012

SN - 9783030553258

T3 - Communications in Computer and Information Science

SP - 162

EP - 177

BT - Parallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers

A2 - Sokolinsky, Leonid

A2 - Zymbler, Mikhail

PB - Springer Gabler

T2 - 14th International Scientific Conference on Parallel Computational Technologies, PCT 2020

Y2 - 27 May 2020 through 29 May 2020

ER -

ID: 24954840