Journal Article10.1137/0914024
A multiresolution method for distributed parameter estimation
TL;DR: It is shown how the method of scale-by-scale multiresolution yields robust and fast convergence and gives a natural regularization approach which is complementary to Tikhonov's regularization.
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Abstract: A multiresolution method for distributed parameter estimation (or inverse problems) is studied numerically. The identification of the coefficient of an elliptic equation in one dimension is considered as our model problem. First, multiscale bases are used to analyze the degree of ill-posedness of the inverse problem. Second, based on some numerical results, it is shown that the method of scale-by-scale multiresolution yields robust and fast convergence. Finally, it is shown how the method gives a natural regularization approach which is complementary to Tikhonov’s regularization.
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Estimation Techniques for Distributed Parameter Systems
Harvey Thomas Banks,Karl Kunisch +1 more
- 01 Jan 1989
TL;DR: Inverse problems in the study of flexible structures as discussed by the authors have been identified in many applications, e.g., in ecology and lake and sea sedimentation analysis, as well as in the analysis of linear parabolic systems.
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Inverse Problems for Partial Differential Equations
TL;DR: In this paper, a workshop brought together mathematicians engaged in dif- ferent aspects of inverse problems for partial differential equations for impedance tomography and scattering theory as well as new developments such as interior transmission eigenvalues were discussed.