Properties of Worst-Case GMRES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00421797" target="_blank" >RIV/67985807:_____/13:00421797 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/13091066X" target="_blank" >http://dx.doi.org/10.1137/13091066X</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/13091066X" target="_blank" >10.1137/13091066X</a>

Result language
angličtina
Original language name
Properties of Worst-Case GMRES
Original language description
In the convergence analysis of the GMRES method for a given matrix A, one quantity of interest is the largest possible residual norm that can be attained, at a given iteration step k, over all unit norm initial vectors. This quantity is called the worst-case GMRES residual norm for A and k. We show that the worst case behavior of GMRES for the matrices A and A transposed is the same, and we analyze properties of initial vectors for which the worst-case residual norm is attained. In particular, we provethat such vectors satisfy a certain "cross equality". We show that the worst-case GMRES polynomial may not be uniquely determined, and we consider the relation between the worst-case and the ideal GMRES approximations, giving new examples in which the inequality between the two quantities is strict at all iteration steps k greater than 3.
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/GA13-06684S" target="_blank" >GA13-06684S: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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