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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - 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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2017

Confidentiality

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

Name of the periodical

Applications of Mathematics

ISSN

0862-7940

e-ISSN

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Volume of the periodical

62

Issue of the periodical within the volume

6

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

23

Pages from-to

537-559

UT code for WoS article

000419946700002

EID of the result in the Scopus database

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