A new version of a preconditioning method for certain two-by-two block matrices with square blocks
Result description
Two-by-two block matrices with square matrix blocks arise in many important appli-cations. Since the problems are of large scale, iterative solution methods must beused. Thereby the choice of an efficient and robust preconditioner is crucial. Thispaper presents two earlier used such preconditioners followed by a novel precondi-tioner based on transforming the given matrix to a proper form. Sharp eigenvalueestimates are derived. The condition numbers of each of the three methods are robustwith respect to all parameters involved, including the mesh parameter. Therefore, thepreconditioners are suitable for a variety of problems where such matrix structuresarise. The performance of the methods are also compared numerically on a set of testproblems.
Keywords
square block matricescomplex to realpreconditionertransformed matrixrobustness
The result's identifiers
Result code in IS VaVaI
Result on the web
https://link.springer.com/article/10.1007%2Fs10543-018-0741-x
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
A new version of a preconditioning method for certain two-by-two block matrices with square blocks
Original language description
Two-by-two block matrices with square matrix blocks arise in many important appli-cations. Since the problems are of large scale, iterative solution methods must beused. Thereby the choice of an efficient and robust preconditioner is crucial. Thispaper presents two earlier used such preconditioners followed by a novel precondi-tioner based on transforming the given matrix to a proper form. Sharp eigenvalueestimates are derived. The condition numbers of each of the three methods are robustwith respect to all parameters involved, including the mesh parameter. Therefore, thepreconditioners are suitable for a variety of problems where such matrix structuresarise. The performance of the methods are also compared numerically on a set of testproblems.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
BIT Numerical Mathematics
ISSN
1572-9125
e-ISSN
—
Volume of the periodical
59
Issue of the periodical within the volume
2
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
22
Pages from-to
321-342
UT code for WoS article
000472842600001
EID of the result in the Scopus database
2-s2.0-85058640749
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2019