Parallel combined chebyshev and least squares iterations in the krylov subspaces

Yana Gurieva, Valery Il’in

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

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.

Original languageEnglish
Title of host publicationParallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers
EditorsLeonid Sokolinsky, Mikhail Zymbler
PublisherSpringer Gabler
Pages162-177
Number of pages16
ISBN (Print)9783030553258
DOIs
Publication statusPublished - 1 Jan 2020
Event14th International Scientific Conference on Parallel Computational Technologies, PCT 2020 - Perm, Russian Federation
Duration: 27 May 202029 May 2020

Publication series

NameCommunications in Computer and Information Science
Volume1263 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference14th International Scientific Conference on Parallel Computational Technologies, PCT 2020
CountryRussian Federation
CityPerm
Period27.05.202029.05.2020

Keywords

  • Anderson acceleration
  • Chebyshev iterative algorithms
  • Convergence of iterations
  • Krylov subspaces
  • Least squares
  • Numerical experiments
  • Numerical stability

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