On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces: On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces

Description

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.

Links & Downloads

1. urn:nbn:de:bsz:ch1-199801185
2. https://monarch.qucosa.de/id/qucosa%3A17493
3. https://monarch.qucosa.de/api/qucosa%3A17493/attachment/ATT-0/
4. https://monarch.qucosa.de/api/qucosa%3A17493/attachment/ATT-1/
5. https://monarch.qucosa.de/api/qucosa%3A17493/attachment/ATT-2/
6. https://monarch.qucosa.de/api/qucosa%3A17493/attachment/ATT-3/

Tags

info:eu-repo/classification/ddc/510

ddc:510

Nonlinear inverse problems

oerator equations

ill-posedness

stability estimates

local ill-posedness

Frechet derivative

linearized problem

compact operators

integral equations

parameter identification

MSC 65J20

MSC 47H15

MSC 65J10

MSC 65J15

MSC 65R30

MSC 45G10

Additional Fields

Identifer	oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:17493
Date	30 October 1998
Creators	Hofmann, B.
Publisher	Technische Universität Chemnitz
Source Sets	Hochschulschriftenserver (HSSS) der SLUB Dresden
Language	English
Detected Language	English
Type	doc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
Rights	info:eu-repo/semantics/openAccess