On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00537319" target="_blank" >RIV/67985807:_____/20:00537319 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11160/20:10417885
Result on the web
<a href="http://dx.doi.org/10.1007/s11075-019-00846-z" target="_blank" >http://dx.doi.org/10.1007/s11075-019-00846-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11075-019-00846-z" target="_blank" >10.1007/s11075-019-00846-z</a>
Alternative languages
Result language
angličtina
Original language name
On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES
Original language description
The paper gives a characterization of all linear systems such that when restarted GMRES is applied, prescribed admissible residual norms and (harmonic) Ritz values for all iterations inside the individual cycles are generated. Additionally, the system matrices can have any nonzero eigenvalues. The total number of GMRES iterations inside all cycles considered is assumed to be smaller than the system size. It is shown that stagnation at the end of a restart cycle must be mirrored at the beginning of the next cycle and that this is the only restriction for prescribed residual norms of restarted GMRES. The relation between prescribed residual norms of restarted GMRES and those of the corresponding full GMRES process is studied and linear systems are given where full and restarted GMRES give the same convergence history.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerical Algorithms
ISSN
1017-1398
e-ISSN
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Volume of the periodical
84
Issue of the periodical within the volume
4
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
24
Pages from-to
1329-1352
UT code for WoS article
000547939900006
EID of the result in the Scopus database
2-s2.0-85076567124