Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

We introduce and analyze 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. In a first step, we simply combi...

Adaptive Wavelet Galerkin Methods for Linear Inverse Problems

Wavelet-galerkin Methods for Ill-posed Problems

| Projection methods based on wavelet functions combine optimal convergence rates with algorithmic eeciency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguel...

Adaptive wavelet methods for saddle point problems

Recently, adaptive wavelet stratégies for symmetrie, positive definite operators have been introduced that were proven to converge. This paper is devoted to the generalization to saddle point problems which are also symmetrie, but indefinite. Firstly, we investigate a posteriori error estimâtes and generalize the known adaptive wavelet strategy to saddle point problems. The convergence of this ...

Adaptive Wavelet Galerkin