Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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
Result continuities
Project
<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerische Mathematik
ISSN
0029-599X
e-ISSN
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Volume of the periodical
146
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
34
Pages from-to
335-368
UT code for WoS article
000563156700001
EID of the result in the Scopus database
2-s2.0-85089871065