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Inverse and Ill-posed Problems Volume 297 (Theory and Applications) by Kabanikhin, Sergey I. is a scholarly article available to read on EtoBox.

What is Inverse and Ill-posed Problems Volume 297 (Theory and Applications) about?

The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem"

Author

Kabanikhin, Sergey I.

Publisher

Saur, K. G., Verlag. ein Imprint der Walter de Gruyter GmbH

Published

2011

Language

EN

ISBN

9783110224009