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Regula falsi based automatic regularization method for PDE constrained optimization.
- Source :
-
Journal of Computational & Applied Mathematics . Mar2019, Vol. 348, p14-25. 12p. - Publication Year :
- 2019
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 348
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 133149734
- Full Text :
- https://doi.org/10.1016/j.cam.2018.08.050