Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F12%3A00382221" target="_blank" >RIV/67985807:_____/12:00382221 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/110843666" target="_blank" >http://dx.doi.org/10.1137/110843666</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/110843666" target="_blank" >10.1137/110843666</a>

Result language
angličtina
Original language name
Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES
Original language description
We show that arbitrary convergence behavior of Ritz values is possible in the Arnoldi method, and we give two parametrizations of the class of matrices with initial Arnoldi vectors that generate prescribed Ritz values (in all iterations). The second parametrization enables us to prove that any GMRES residual norm history is possible with any prescribed Ritz values (in all iterations), provided that we treat the stagnation case appropriately.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/IAA100300802" target="_blank" >IAA100300802: Theory of Krylov subspace methods and its relationship to other mathematical disciplines</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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