Inverse and Illposed Problems Theory and Applications
The theory of illposed 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 illposed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attentio...
Main Author:  

Format:  eBook 
Language:  English 
Published: 
Berlin
De Gruyter
[2011]©2011, 2011

Series:  Inverse and IllPosed Problems Series

Subjects:  
Online Access:  
Collection:  DeGruyter MPG Collection  Collection details see MPG.ReNa 
Summary:  The theory of illposed 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 illposed 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. Illposed problems occur everywhere and it is unreasonable to ignore them. Unlike illposed 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 (wellposed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly illposed. This book was conceived as a textbook on the foundations of the theory of inverse and illposed 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 illposed problems but we hope that it will be useful to anyone who is interested in the subject The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of illposed problems. Nowadays, the terms "inverse problem" and "illposed problem" are inextricably linked to each other. Inverse and illposed 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. 

Item Description:  Mode of access: Internet via World Wide Web 
Physical Description:  475 p. 
ISBN:  9783110224016 