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

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 struc...

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Bibliographic Details
Main Authors: Maaß, Peter, Pereverzev, Sergei V., Ramlau, Ronny, Solodky, Sergei G.
Format: Others
Language:English
Published: Universität Potsdam 1998
Subjects:
Physics
Online Access:http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14739
http://opus.kobv.de/ubp/volltexte/2007/1473/
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spelling ndltd-Potsdam-oai-kobv.de-opus-ubp-14732013-01-08T00:56:16Z An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection Maaß, Peter Pereverzev, Sergei V. Ramlau, Ronny Solodky, Sergei G. Physics 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. Universität Potsdam Mathematisch-Naturwissenschaftliche Fakultät. Institut für Physik und Astronomie Wissenschaftliche Einrichtungen. Interdisziplinäres Zentrum Dynamik komplexer Systeme 1998 Preprint application/pdf urn:nbn:de:kobv:517-opus-14739 http://opus.kobv.de/ubp/volltexte/2007/1473/ eng http://opus.kobv.de/ubp/doku/urheberrecht.php
collection NDLTD
language English
format Others
sources NDLTD
topic Physics
spellingShingle Physics
Maaß, Peter
Pereverzev, Sergei V.
Ramlau, Ronny
Solodky, Sergei G.
An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
description 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 Maaß, Peter
Pereverzev, Sergei V.
Ramlau, Ronny
Solodky, Sergei G.
author_facet Maaß, Peter
Pereverzev, Sergei V.
Ramlau, Ronny
Solodky, Sergei G.
author_sort Maaß, Peter
title An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
title_short An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
title_full An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
title_fullStr An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
title_full_unstemmed An adaptive discretization for Tikhonov-Phillips regularization with a posteriori parameter selection
title_sort adaptive discretization for tikhonov-phillips regularization with a posteriori parameter selection
publisher Universität Potsdam
publishDate 1998
url http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14739
http://opus.kobv.de/ubp/volltexte/2007/1473/
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