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On the Autoconvolution Equation and Total Variation Constraints

This paper is concerned with the numerical analysis of the autoconvolution equation
$x*x=y$ restricted to the interval [0,1]. We present a discrete constrained least
squares approach and prove its convergence in $L^p(0,1),1<p<\infinite$ , where
the regularization is based on a prescribed bound for the total variation of admissible
solutions. This approach includes the case of non-smooth solutions possessing jumps.
Moreover, an adaption to the Sobolev space $H^1(0,1)$ and some remarks on monotone
functions are added. The paper is completed by a numerical case study concerning
the determination of non-monotone smooth and non-smooth functions x from the autoconvolution
equation with noisy data y.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801196
Date30 October 1998
CreatorsFleischer, G., Gorenflo, R., Hofmann, B.
ContributorsTU Chemnitz, Fakultät für Mathematik
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, application/x-dvi, application/postscript, text/plain, application/zip

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