Compress-and-restart block Krylov subspace methods for Sylvester matrix equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10422163" target="_blank" >RIV/00216208:11320/21:10422163 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=D3DS9qMcNC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=D3DS9qMcNC</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/nla.2339" target="_blank" >10.1002/nla.2339</a>
Alternative languages
Result language
angličtina
Original language name
Compress-and-restart block Krylov subspace methods for Sylvester matrix equations
Original language description
Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov subspace methods provide a major reduction in iteration counts over polynomial block KSMs, they also require reliable solvers for the coefficient matrices, and these solvers are often iterative methods themselves. It is not hard to devise scenarios in which the available memory, and consequently the dimension of the Krylov subspace, is limited. In such scenarios for linear systems and eigenvalue problems, restarting is a well-explored technique for mitigating memory constraints. In this work, such restarting techniques are applied to polynomial KSMs for matrix equations with a compression step to control the growing rank of the residual. An error analysis is also per- formed, leading to heuristics for dynamically adjusting the basis size in each restart cycle. A panel of numerical experiments demonstrates the effectiveness of the new method with respect to extended block KSMs.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Linear Algebra with Applications
ISSN
1070-5325
e-ISSN
—
Volume of the periodical
28
Issue of the periodical within the volume
1
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
e2339
UT code for WoS article
000578664700001
EID of the result in the Scopus database
2-s2.0-85092411794