TY  - INPR
A1  - Freeden, Willi
A1  - Schneider, F.
T1  - Regularization Wavelets and Multiresolution
N2  - Many problems arising in (geo)physics and technology can be formulated as compact operator equations of the first kind \(A F = G\). Due to the ill-posedness of the equation a variety of regularization methods are in discussion for an approximate solution, where particular emphasize must be put on balancing the data and the approximation error. In doing so one is interested in optimal parameter choice strategies. In this paper our interest lies in an efficient algorithmic realization of a special class of regularization methods. More precisely, we implement regularization methods based on filtered singular value decomposition as a wavelet analysis. This enables us to perform, e.g., Tikhonov-Philips regularization as multiresolution. In other words, we are able to pass over from one regularized solution to another one by adding or subtracting so-called detail information in terms of wavelets. It is shown that regularization wavelets as proposed here are efficiently applicable to a future problem in satellite geodesy, viz. satellite gravity gradiometry.
T3  - Berichte der Arbeitsgruppe Technomathematik (AGTM Report) - 174 
KW  - compact operator equation
KW  - regularization wavelets
KW  - mutiresolution
Y1  - 1997
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/609
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-5783
N1  - Altdaten, kein Volltext verfügbar ; Printversion in Bereichsbibliothek Mathematik vorhanden: MAT 144/620-174
ER  -