Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00534464" target="_blank" >RIV/68145535:_____/20:00534464 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs00211-020-01143-x" target="_blank" >https://link.springer.com/article/10.1007%2Fs00211-020-01143-x</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00211-020-01143-x" target="_blank" >10.1007/s00211-020-01143-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Popis výsledku v původním jazyce

Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties,nsuch as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

Název v anglickém jazyce

Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks

Popis výsledku anglicky

Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties,nsuch as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Numerische Mathematik

ISSN

0029-599X

e-ISSN

—

Svazek periodika

146

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

34

Strana od-do

335-368

Kód UT WoS článku

000563156700001

EID výsledku v databázi Scopus

2-s2.0-85089871065