On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11160/20:10417885

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Numerical Algorithms

ISSN

1017-1398

e-ISSN

—

Svazek periodika

84

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

24

Strana od-do

1329-1352

Kód UT WoS článku

000547939900006

EID výsledku v databázi Scopus

2-s2.0-85076567124