TY  - INPR
A1  - Maaß, Peter
A1  - Pereverzev, Sergei V.
A1  - Ramlau, Ronny
A1  - Solodky, Sergei G.
T1  - An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
N2  - The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
T3  - NLD Preprints - 48 
Y1  - 1998
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14739
ER  - 
TY  - INPR
A1  - Maaß, Peter
A1  - Rieder, Andreas
T1  - Wavelet-accelerated Tikhonov-Phillips regularization with applications
N2  - Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}
T3  - NLD Preprints - 30 
Y1  - 1996
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-14104
ER  - 
TY  - INPR
A1  - Dicken, Volker
A1  - Maaß, Peter
T1  - Wavelet-Galerkin methods for ill-posed problems
N2  - Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. 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-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
T3  - NLD Preprints - 22 
Y1  - 1995
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-13890
ER  -