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Title
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Regula falsi based automatic regularization method for PDE constrained optimization
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Author
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Abstract
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| Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related-to-its solution. This can be-seen as a constrained minimization problem where one wishes to minimize the mismatch between the observed data and the model predictions, including an extra regularization term, and use the PDE as a constraint. Often, a suitable regularization parameter is determined by solving the problem for a whole range of parameters-e.g. using the L-curve-which is computationally very expensive. In this paper we derive two methods that simultaneously solve the inverse problem and determine a suitable value for the regularization parameter. The first one is a direct generalization of the Generalized Arnoldi Tikhonov method for linear inverse problems. The second method is a novel method based on similar ideas, but with a number of advantages for nonlinear problems. (C) 2018 Elsevier B.V. All rights reserved. |
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Language
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English
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Source (journal)
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Journal of computational and applied mathematics. - Antwerp, 1975, currens
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Publication
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Antwerp
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2019
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ISSN
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0377-0427
[print]
1879-1778
[online]
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DOI
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10.1016/J.CAM.2018.08.050
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Volume/pages
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348
(2019)
, p. 14-25
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ISI
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000452941400002
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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