Publication
Title
Regula falsi based automatic regularization method for PDE constrained optimization
Author
Abstract
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.
Language
English
Source (journal)
Journal of computational and applied mathematics. - Antwerp
Publication
Antwerp : 2019
ISSN
0377-0427
Volume/pages
348 (2019) , p. 14-25
ISI
000452941400002
Full text (Publisher's DOI)
Full text (open access)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identifier
Creation 18.01.2019
Last edited 15.11.2022
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