Prescribing the behavior of early terminating GMRES and Arnoldi iterations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F14%3A00390278" target="_blank" >RIV/67985807:_____/14:00390278 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11075-013-9695-x" target="_blank" >http://dx.doi.org/10.1007/s11075-013-9695-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-013-9695-x" target="_blank" >10.1007/s11075-013-9695-x</a>

Result language
angličtina
Original language name
Prescribing the behavior of early terminating GMRES and Arnoldi iterations
Original language description
We generalize and extend results of the series of papers by Greenbaum and Strakoš (IMA Vol Math Appl 60:95?118, 1994), Greenbaum et al. (SIAM J Matrix Anal Appl 17(3):465?469, 1996), Arioli et al. (BIT 38(4):636?643, 1998) and Duintjer Tebbens and Meurant (SIAM J Matrix Anal Appl 33(3):958?978, 2012). They show how to construct matrices with right-hand sides generating a prescribed GMRES residual norm convergence curve as well as prescribed Ritz values in all iterations, including the eigenvalues, and give parametrizations of the entire class of matrices and right-hand sides with these properties. These results assumed that the underlying Arnoldi orthogonalization processes are breakdown-free and hence considered non-derogatory matrices only. We extendthe results with parametrizations of classes of general nonsingular matrices with right-hand sides allowing the early termination case and also give analogues for the early termination case of other results related to the theory develope
Czech name
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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
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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
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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