In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems
in a Hilbert space setting. We define local ill-posedness of a nonlinear operator
equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear
problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an
appropriate ill-posedness concept for the linarized equation we define intrinsic
ill-posedness for linear operator equations $Ax = y$ and compare this approach with
the ill-posedness definitions due to Hadamard and Nashed.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801185 |
| Date | 30 October 1998 |
| Creators | 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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