Parallel combined chebyshev and least squares iterations in the krylov subspaces

Yana Gurieva, Valery Il’in

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииParallel Computational Technologies - 14th International Conference, PCT 2020, Revised Selected Papers
РедакторыLeonid Sokolinsky, Mikhail Zymbler
ИздательSpringer Gabler
Страницы162-177
Число страниц16
ISBN (печатное издание)9783030553258
DOI
СостояниеОпубликовано - 1 янв 2020
Событие14th International Scientific Conference on Parallel Computational Technologies, PCT 2020 - Perm, Российская Федерация
Продолжительность: 27 мая 202029 мая 2020

Серия публикаций

НазваниеCommunications in Computer and Information Science
Том1263 CCIS
ISSN (печатное издание)1865-0929
ISSN (электронное издание)1865-0937

Конференция

Конференция14th International Scientific Conference on Parallel Computational Technologies, PCT 2020
СтранаРоссийская Федерация
ГородPerm
Период27.05.202029.05.2020

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