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An Introduction to the Mathematical Theory of Inverse Problems

By Andreas Kirsch

An Introduction to the Mathematical Theory of Inverse Problems Media & Communication

An Introduction to the Mathematical Theory of Inverse Problems

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Description
This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography. The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples. The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness and continuous dependence on parameters. Then some theoretical results as well as numerical procedures for the inverse problems are discussed. The choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students. Basic knowledge of real analysis is assumed. In this new edition, the Factorization Method is included as one of the prominent members in this monograph. Since the Factorization Method is particularly simple for the problem of EIT and this field has attracted a lot of attention during the past decade a chapter on EIT has been added in this monograph as Chapter 5 while the chapter on inverse scattering theory is now Chapter 6.The main changes of this second edition compared to the first edition concern only Chapters 5 and 6 and the Appendix A. Chapter 5 introduces  the reader to the inverse problem of electrical impedance tomography.
Product details
Edition:
2
Number of Pages:
324
Release Date:
2011-04-06
Publication Date:
2011-09-30
Publisher:
Springer-Verlag GmbH
Languages:
Original: English
ISBN10:
1441984739
ISBN13:
9781441984739
Weight:
649 g
Height:
161 cm
Width:
244 cm
Thickness:
25 cm
Preview Link:
http://www.blickinsbuch.de/viewer/cm/access.php?djMxNTY9NDIwMzQ1MjgxNyZ2NzM3Nj05NzgxNDQxOTg0NzM5
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The items bear minimal signs of past use, such as light scratches or memories in the form of markings. These signs of wear give the items a charming character and tell stories of their previous owners, while not affecting their functionality.
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