Efficient iterative solvers for a complex valued two-by-two block linear system with application to parabolic optimal control problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68145535%3A_____%2F20%3A00534407" target="_blank" >RIV/68145535:_____/20:00534407 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0168927419303198?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0168927419303198?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2019.11.011" target="_blank" >10.1016/j.apnum.2019.11.011</a>
Alternative languages
Result language
angličtina
Original language name
Efficient iterative solvers for a complex valued two-by-two block linear system with application to parabolic optimal control problems
Original language description
In this paper, we are concerned with the efficient iterative solution of time-harmonic parabolic optimal control problems. A robust parameterized preconditioner is proposed for the arising complex valued two-by-two block linear system related to the first-order optimality conditions. Practical parameter choice strategies are considered for the new preconditioner to improve the performance of the original preconditioner within Krylov subspace acceleration. Moreover, a nonstationary second-order iteration method is devised from the parameterized preconditioner within Chebyshev acceleration. Based on a detailed spectral analysis of the preconditioned matrix, convergence rates are analyzed for both the established Krylov subspace and Chebyshev acceleration methods. Due to the tight and problem independent eigenvalue distributions of the preconditioned matrix, the implementation of the Chebyshev acceleration method is parameter free and the obtained iteration error bounds of both methods result in almost parameter independent convergence rates. Numerical experiments are presented to confirm the robustness and effectiveness of the parameterized preconditioner for both Krylov subspace and Chebyshev accelerations and improvement compared to earlier results.
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
Applied Numerical Mathematics
ISSN
0168-9274
e-ISSN
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Volume of the periodical
152
Issue of the periodical within the volume
June 2020
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
24
Pages from-to
422-445
UT code for WoS article
000519653600027
EID of the result in the Scopus database
2-s2.0-85075865990