EFFICIENT SOLUTION OF PARAMETER IDENTIFICATION PROBLEMS WITH H1 REGULARIZATION
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10490704" target="_blank" >RIV/00216208:11320/24:10490704 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZKoOmR9bxx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZKoOmR9bxx</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/22M1520591" target="_blank" >10.1137/22M1520591</a>
Alternative languages
Result language
angličtina
Original language name
EFFICIENT SOLUTION OF PARAMETER IDENTIFICATION PROBLEMS WITH H1 REGULARIZATION
Original language description
We consider the identification of spatially distributed parameters under H 1 regularization. Solving the associated minimization problem by Gauss--Newton iteration results in linearized problems to be solved in each step that can be cast as boundary value problems involving a low-rank modification of the Laplacian. Using an algebraic multigrid as a fast Laplace solver, the Sherman-Morrison--Woodbury formula can be employed to construct a preconditioner for these linear problems which exhibits excellent scaling w.r.t. the relevant problem parameters. We first develop this approach in the functional setting, thus obtaining a consistent methodology for selecting boundary conditions that arise from the H 1 regularization. We then construct a method for solving the discrete linear systems based on combining any fast Poisson solver with the Woodbury formula. The efficacy of this method is then demonstrated with scaling experiments. These are carried out for a common nonlinear parameter identification problem arising in electrical resistivity tomography.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal of Scientific Computing
ISSN
1064-8275
e-ISSN
1095-7197
Volume of the periodical
46
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
"A1160"-"A1185"
UT code for WoS article
001291134400005
EID of the result in the Scopus database
2-s2.0-85191579856