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121012 r ||| eng |
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|a 9783110224016
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|a QA378.5
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|a Kabanikhin, Sergey I.
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| 245 |
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|a Inverse and Ill-posed Problems
|h Elektronische Ressource
|b Theory and Applications
|c Sergey I. Kabanikhin
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| 260 |
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|a Berlin
|b De Gruyter
|c [2011]©2011, 2011
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| 300 |
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|a 475 p.
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| 653 |
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|a Integralgleichung
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| 653 |
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|a Integral Equation
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| 653 |
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|a Boundary value problems / Improperly posed problems
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| 653 |
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|a Inverse Problem
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| 653 |
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|a Ill-posed Problems
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| 653 |
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|a MATHEMATICS / Applied / bisacsh
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| 653 |
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|a Differential Equation
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| 653 |
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|a Lineare Operatorgleichung
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| 653 |
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|a Inverse problems (Differential equations)
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| 653 |
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|a Regularization
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| 653 |
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|a Differentialgleichung
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| 653 |
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|a Inverses Problem
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| 653 |
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|a Nichtlineare Operatorgleichung
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b GRUYMPG
|a DeGruyter MPG Collection
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| 490 |
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|a Inverse and Ill-Posed Problems Series
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| 500 |
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|a Mode of access: Internet via World Wide Web
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| 028 |
5 |
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|a 10.1515/9783110224016
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| 773 |
0 |
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|t DGBA Backlist Mathematics English Language 2000-2014
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| 773 |
0 |
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|t DGBA Backlist Complete English Language 2000-2014 PART1
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| 773 |
0 |
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|t DGBA Mathematics 2000 - 2014
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| 773 |
0 |
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|t E-BOOK GESAMTPAKET / COMPLETE PACKAGE 2011
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| 773 |
0 |
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|t E-BOOK PACKAGE ENGLISH LANGUAGES TITLES 2011
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| 773 |
0 |
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|t E-BOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2011
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| 856 |
4 |
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|u https://www.degruyter.com/doi/book/10.1515/9783110224016?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 515/.357
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| 520 |
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|a 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.
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| 520 |
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|a This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject
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| 520 |
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|a 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" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe.
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