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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801196 |
| Date | 30 October 1998 |
| Creators | Fleischer, G., Gorenflo, R., Hofmann, B. |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:preprint |
| Format | application/pdf, application/x-dvi, application/postscript, text/plain, application/zip |
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