Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00524496" target="_blank" >RIV/68145535:_____/20:00524496 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/10.1137/19M1272469" target="_blank" >https://epubs.siam.org/doi/10.1137/19M1272469</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/19M1272469" target="_blank" >10.1137/19M1272469</a>
Alternative languages
Result language
angličtina
Original language name
Admissible and Attainable Convergence Behavior of Block Arnoldi and GMRES
Original language description
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.nnnn
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN
1095-7162
e-ISSN
—
Volume of the periodical
41
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
23
Pages from-to
464-486
UT code for WoS article
000546981500005
EID of the result in the Scopus database
2-s2.0-85084943132