On the parallel least square approaches in the krylov subspaces

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

Аннотация

We consider different parallel versions of the least squares methods in the Krylov subspaces which are based on computing various basis vectors. These algorithms are used for solving very large real, non-symmetric, in gerenal, sparse systems of linear algebraic equations (SLAEs) which arise in grid approximations of multi-dimensional boundary value problems. In particular, the Chebyshev acceleration approach, steepest descent and minimal residual, conjugate gradient and conjugate residual are applied as preliminary iterative processes. The resulting minimization of residuals is provided by the block, or implicit, orthogonalization procedures. The properties of the Krylov approaches proposed are analysed in the “pure form”, i.e. without preconditioning. The main criteria of parallelezation are estimated. The convergence rate and stability of the algorithms are demonstated on the results of numerical experiments for the model SLAEs which present the exponential fitting approximation of diffusion-convection equations on the meshes with various steps and with different coefficients.

Язык оригиналаанглийский
Название основной публикацииSupercomputing - 3rd Russian Supercomputing Days, RuSCDays 2017, Revised Selected Papers
Редакторы Voevodin, S Sobolev
ИздательSpringer-Verlag GmbH and Co. KG
Страницы168-180
Число страниц13
Том793
ISBN (печатное издание)9783319712543
DOI
СостояниеОпубликовано - 2017
Событие3rd Russian Supercomputing Days Conference, RuSCDays 2017 - Moscow, Российская Федерация
Продолжительность: 25 сен 201726 сен 2017

Серия публикаций

НазваниеCommunications in Computer and Information Science
Том793
ISSN (печатное издание)1865-0929

Конференция

Конференция3rd Russian Supercomputing Days Conference, RuSCDays 2017
СтранаРоссийская Федерация
ГородMoscow
Период25.09.201726.09.2017

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    Il’in, V. P. (2017). On the parallel least square approaches in the krylov subspaces. В Voevodin, & S. Sobolev (Ред.), Supercomputing - 3rd Russian Supercomputing Days, RuSCDays 2017, Revised Selected Papers (Том 793, стр. 168-180). (Communications in Computer and Information Science; Том 793). Springer-Verlag GmbH and Co. KG. https://doi.org/10.1007/978-3-319-71255-0_13