Any Admissible Harmonic Ritz Value Set is Possible for GMRES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F17%3A00477885" target="_blank" >RIV/67985807:_____/17:00477885 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11160/17:10365008
Result on the web
<a href="http://etna.mcs.kent.edu/volumes/2011-2020/vol47/abstract.php?vol=47&pages=37-56" target="_blank" >http://etna.mcs.kent.edu/volumes/2011-2020/vol47/abstract.php?vol=47&pages=37-56</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Any Admissible Harmonic Ritz Value Set is Possible for GMRES
Original language description
It is known that the harmonic Ritz values are the zeros of the GMRES residual polynomials. In this paper we show that any decreasing GMRES residual norm history is possible with any prescribed finite harmonic Ritz values in every iteration of the GMRES process. In addition, we characterize the admissible harmonic Ritz values when GMRES stagnates during some iterations, and show that with any prescribed, in this sense admissible harmonic Ritz values, any non-increasing GMRES residual norm history is possible. We also present a parameterization of the class of matrices and right-hand sides yielding prescribed GMRES residual norms and prescribed admissible harmonic Ritz values.
Czech name
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Czech description
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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

Project
<a href="/en/project/GA13-06684S" target="_blank" >GA13-06684S: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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