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2019 | OriginalPaper | Buchkapitel

4. Ill-Posed Problems

verfasst von : David Colton, Rainer Kress

Erschienen in: Inverse Acoustic and Electromagnetic Scattering Theory

Verlag: Springer International Publishing

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Abstract

As previously mentioned, for problems in mathematical physics Hadamard postulated three requirements: a solution should exist, the solution should be unique, and the solution should depend continuously on the data. The third postulate is motivated by the fact that in all applications the data will be measured quantities. Therefore, one wants to make sure that small errors in the data will cause only small errors in the solution. A problem satisfying all three requirements is called well-posed. Otherwise, it is called ill-posed.

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Metadaten
Titel
Ill-Posed Problems
verfasst von
David Colton
Rainer Kress
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-30351-8_4