Wavelet-Galerkin methods for ill-posed problems

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Abstract
Projection methods based on wavelet functions combine optimal convergence rates withalgorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and resultsfrom the general theory of regularization methods. Moreover, adaptive strategies can be incorporatedstill leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelettedecompositions enable the realization of especially fast algorithms for certain operators.1....

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