On investigating GMRES convergence using unitary matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10281620" target="_blank" >RIV/00216208:11320/14:10281620 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/14:00427016 RIV/00216208:11160/14:10281620
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0024379514001116" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0024379514001116</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2014.02.044" target="_blank" >10.1016/j.laa.2014.02.044</a>
Alternative languages
Result language
angličtina
Original language name
On investigating GMRES convergence using unitary matrices
Original language description
For a given matrix A and right-hand side b, this paper investigates unitary matrices generating, with some right-hand sides c, the same GMRES residual norms as the pair (A, b). We give characterizations of this class of unitary matrices and point out therelationship with Krylov subspaces and Krylov residual subspaces for the pair (A, b). We investigate the eigenvalues of these unitary matrices in relation to the convergence behavior of GMRES for the pair (A, b) and describe the indispensable role of the eigenvector information. We conclude with a formula for the GMRES residual norms generated by a normal matrix B in terms of its eigenvalues and components of the right-hand side c in the eigenvector basis.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
450
Issue of the periodical within the volume
June
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
83-107
UT code for WoS article
000336695700007
EID of the result in the Scopus database
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