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Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES
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SYSNO ASEP 0524496 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES Author(s) Kubínová, Marie (UGN-S)
Soothalter, K. M. (IE)Number of authors 2 Source Title SIAM Journal on Matrix Analysis and Applications. - : SIAM Society for Industrial and Applied Mathematics - ISSN 0895-4798
Roč. 41, č. 2 (2020), s. 464-486Number of pages 23 s. Publication form Online - E Language eng - English Country US - United States Keywords block Krylov subspace methods ; multiple right-hand sides ; block GMRES ; convergence ; spectrum ; block companion matrix Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects LQ1602 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Method of publishing Limited access Institutional support UGN-S - RVO:68145535 UT WOS 000546981500005 EID SCOPUS 85084943132 DOI 10.1137/19M1272469 Annotation It is well-established that any nonincreasing convergence curve is possible for GMRES and a family of pairs $(A,b)$ can be constructed for which GMRES exhibits a given convergence curve with $A$ having arbitrary spectrum. No analogue of this result has been established for block GMRES, wherein multiple right-hand sides are considered. By reframing the problem as a single linear system over a ring of square matrices, we develop convergence results for block Arnoldi and block GMRES. In particular, we show what convergence behavior is admissible for block GMRES and how the matrices and right-hand sides producing any admissible behavior can be constructed. Moreover, we show that the convergence of the block Arnoldi method for eigenvalue approximation can be almost fully independent of the convergence of block GMRES for the same coefficient matrix and the same starting vectors.
Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2021 Electronic address https://epubs.siam.org/doi/10.1137/19M1272469
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