Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F17%3A00482832" target="_blank" >RIV/68145535:_____/17:00482832 - isvavai.cz</a>

Výsledek na webu

<a href="http://articles.math.cas.cz/10.21136/AM.2017.0222-17/?type=F" target="_blank" >http://articles.math.cas.cz/10.21136/AM.2017.0222-17/?type=F</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2017.0222-17" target="_blank" >10.21136/AM.2017.0222-17</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications

Popis výsledku v původním jazyce

Two-by-two block matrices of special form with square matrix blocks arise in important applications, such as in optimal control of partial differential equations and in high order time integration methods. Two solution methods involving very efficient preconditioned matrices, one based on a Schur complement reduction of the given system and one based on a transformation matrix with a perturbation of one of the given matrix blocks are presented. The first method involves an additional inner solution with the pivot matrix block but gives a very tight condition number bound when applied for a time integration method. The second method does not involve this matrix block but only inner solutions with a linear combination of the pivot block and the off-diagonal matrix blocks. Both the methods give small condition number bounds that hold uniformly in all parameters involved in the problem, i.e. are fully robust. The paper presents shorter proofs, extended and new results compared to earlier publications.

Název v anglickém jazyce

Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications

Popis výsledku anglicky

Two-by-two block matrices of special form with square matrix blocks arise in important applications, such as in optimal control of partial differential equations and in high order time integration methods. Two solution methods involving very efficient preconditioned matrices, one based on a Schur complement reduction of the given system and one based on a transformation matrix with a perturbation of one of the given matrix blocks are presented. The first method involves an additional inner solution with the pivot matrix block but gives a very tight condition number bound when applied for a time integration method. The second method does not involve this matrix block but only inner solutions with a linear combination of the pivot block and the off-diagonal matrix blocks. Both the methods give small condition number bounds that hold uniformly in all parameters involved in the problem, i.e. are fully robust. The paper presents shorter proofs, extended and new results compared to earlier publications.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

62

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

23

Strana od-do

537-559

Kód UT WoS článku

000419946700002

EID výsledku v databázi Scopus

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