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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Author:Peter Maaß, Sergei V. Pereverzev, Ronny Ramlau, Sergei G. Solodky
Series (Serial Number):NLD Preprints (paper 048)
Document Type:Preprint
Year of Completion: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
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik