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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 495, Pages 38–43
DOI: https://doi.org/10.31857/S2686954320060223
(Mi danma132)
 

MATHEMATICS

On moment methods in Krylov subspaces

V. P. Il'inab

a Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russian Federation
b Novosibirsk State University, Novosibirsk, Russian Federation
References:
Abstract: Moment methods in Krylov subspaces for solving symmetric systems of linear algebraic equations (SLAEs) are considered. A family of iterative algorithms is proposed based on generalized Lanczos orthogonalization with an initial vector $v^0$ chosen regardless of the initial residual. By applying this approach, a series of SLAEs with the same matrix, but with different right-hand sides can be solved using a single set of basis vectors. Additionally, it is possible to implement generalized moment methods that reduce to block Krylov algorithms using a set of linearly independent guess vectors $v^0,\dots,v^0_m$. The performance of algorithm implementations is improved by reducing the number of matrix multiplications and applying efficient parallelization of vector operations. It is shown that the applicability of moment methods can be extended using preconditioning to various classes of algebraic systems: indefinite, incompatible, asymmetric, and complex, including non-Hermitian ones.
Keywords: moment method, Krylov subspace, parametric Lanczos orthogonalization, conjugate direction algorithms.
Funding agency Grant number
Russian Foundation for Basic Research 18–01–00295
This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00295.
Presented: E. E. Tyrtyshnikov
Received: 02.06.2020
Revised: 02.06.2020
Accepted: 11.11.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 3, Pages 478–482
DOI: https://doi.org/10.1134/S1064562420060241
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: V. P. Il'in, “On moment methods in Krylov subspaces”, Dokl. RAN. Math. Inf. Proc. Upr., 495 (2020), 38–43; Dokl. Math., 102:3 (2020), 478–482
Citation in format AMSBIB
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\by V.~P.~Il'in
\paper On moment methods in Krylov subspaces
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 495
\pages 38--43
\mathnet{http://mi.mathnet.ru/danma132}
\crossref{https://doi.org/10.31857/S2686954320060223}
\zmath{https://zbmath.org/?q=an:7424670}
\elib{https://elibrary.ru/item.asp?id=44367199}
\transl
\jour Dokl. Math.
\yr 2020
\vol 102
\issue 3
\pages 478--482
\crossref{https://doi.org/10.1134/S1064562420060241}
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