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Erscheinungsjahr: 
2002
Schriftenreihe/Nr.: 
SFB 373 Discussion Paper No. 2002,50
Verlag: 
Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin
Zusammenfassung: 
We introduce and analyse numerical methods for the treatment of inverse problems, based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the solution, together with the numerical simplicity of Galerkin methods. Two strategies are proposed: the first one simply combines a thresholding algorithm on the data with a Galerkin inversion on a fixed liner space, while the second one performs the inversion through an adaptive procedure in which a smaller space adapted to the solution is iteratively constructed. For both methods, we recover the same minimax rates achieved by WVD for various function classes modeling the solution.
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