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.
Author details: | Peter Maaß, Sergei V. Pereverzev, Ronny Ramlau, Sergei G. Solodky |
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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 |