Parameter modified versions of preconditioning and iterative inner product free refinement methods for two-by-two block matrices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F19%3A00509852" target="_blank" >RIV/68145535:_____/19:00509852 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0024379519303118" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0024379519303118</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2019.07.024" target="_blank" >10.1016/j.laa.2019.07.024</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Parameter modified versions of preconditioning and iterative inner product free refinement methods for two-by-two block matrices

Popis výsledku v původním jazyce

A special two-by-two block matrix form arises in many important applications. Extending earlier results it is shown that parameter modified versions of a very efficient preconditioner does not improve its rate of convergence. This holds also for iterative refinement methods corresponding to a few fixed steps of the Chebyshev accelerated method. The parameter version can improve the defect-correction method but the convergence of this method is slower than an iterative refinement method with an optimal parameter. The paper includes also a discussion of how one can save computer elapsed times by avoiding use of global inner products such as by use of a Chebyshev accelerated method instead of a Krylov subspace method. Since accurate and even sharp eigenvalue bounds are available, the Chebyshev iteration method converges as fast as the Krylov subspace method.

Název v anglickém jazyce

Parameter modified versions of preconditioning and iterative inner product free refinement methods for two-by-two block matrices

Popis výsledku anglicky

A special two-by-two block matrix form arises in many important applications. Extending earlier results it is shown that parameter modified versions of a very efficient preconditioner does not improve its rate of convergence. This holds also for iterative refinement methods corresponding to a few fixed steps of the Chebyshev accelerated method. The parameter version can improve the defect-correction method but the convergence of this method is slower than an iterative refinement method with an optimal parameter. The paper includes also a discussion of how one can save computer elapsed times by avoiding use of global inner products such as by use of a Chebyshev accelerated method instead of a Krylov subspace method. Since accurate and even sharp eigenvalue bounds are available, the Chebyshev iteration method converges as fast as the Krylov subspace method.

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

2019

Kód důvěrnosti údajů

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

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

582

Číslo periodika v rámci svazku

December 2019

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

403-429

Kód UT WoS článku

000489000000020

EID výsledku v databázi Scopus

2-s2.0-85070910739