We deal with locally ill-posed nonlinear operator equations F(x) = y in L^2(0,1),
where the Fréchet derivatives A = F'(x_0) of the nonlinear forward operator F are
compact linear integral operators A = M ◦ J with a multiplication operator M
with integrable multiplier function m and with the simple integration operator J.
In particular, we give examples of nonlinear inverse problems in natural sciences
and stochastic finance that can be written in such a form with linearizations that
contain multiplication operators. Moreover, we consider the corresponding ill-posed
linear operator equations Ax = y and their degree of ill-posedness. In particular,
we discuss the fact that the noncompact multiplication operator M has only a
restricted influence on this degree of ill-posedness even if m has essential zeros of
various order.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200501261 |
| Date | 07 October 2005 |
| Creators | Hofmann, Bernd |
| Contributors | TU Chemnitz, Fakultät für Mathematik |
| Publisher | Universitätsbibliothek Chemnitz |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:lecture |
| Format | application/pdf, text/plain, application/zip |
| Relation | dcterms:isPartOfhttp://nbn-resolving.de/urn:nbn:de:swb:ch1-200501214 |
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