An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection

  • 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.

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Metadaten
Author details:Peter Maaß, Sergei V. Pereverzev, Ronny Ramlau, Sergei G. Solodky
URN:urn:nbn:de:kobv:517-opus-14739
Publication series (Volume number):NLD Preprints (48)
Publication type:Preprint
Language:English
Publication year:1998
Publishing institution:Universität Potsdam
Release date:2007/07/13
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Zentrale und wissenschaftliche Einrichtungen / Interdisziplinäres Zentrum für Dynamik komplexer Systeme
DDC classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
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