An Introduction to the Mathematical Theory of Inverse Problems (Applied Mathematical Sciences) [Hardcover]

Andreas Kirsch (Author)

Book Description

ISBN-10: 038794530X | ISBN-13: 978-0387945309 | Publication Date: September 26, 1996 | Edition: 1

This book introduces the reader to the area of inverse problems. A relatively new branch of Applied Mathematics, 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.

Editorial Reviews

From the Back Cover

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 three special nonlinear inverse problems in detail - the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), 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.   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.   The book is highly illustrated and contains many exercises. This together with the choice of material and its presentation in the book are new, thus making it particularly suitable for graduate students in mathematics and engineering. --This text refers to an alternate Hardcover edition.

About the Author

Andreas Kirsch is a Professor in the Department of Mathematics at Karlsruhe Institute of Technology. --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 310 pages
• Publisher: Springer; 1 edition (September 26, 1996)
• Language: English
• ISBN-10: 038794530X
• ISBN-13: 978-0387945309
• Product Dimensions: 9.3 x 6.5 x 0.9 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,376,883 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

4.0 out of 5 stars Nice book, September 10, 2001

By 

Richard Bloemenkamp (Delft, the Netherlands) - See all my reviews

This review is from: An Introduction to the Mathematical Theory of Inverse Problems (Applied Mathematical Sciences) (Hardcover)

I disagree with the negative rating that was given by Colin Fox. In my view the book is a well-written introduction to a lot of mathematical terms used in theoretical works on inverse problems. Although the methods may be outdated a little, the mathematical basis of the methods seems to be very good and the examples are easy to understand. The book is focussed on continuous eigenvalue, potential and scattering problems. For discrete inverse problems it is probably wiser to consider a different book. This book helped me to understand the work of mathematicians such as Colton and Kress better. Since I do not have a very mathematical background, I'm curious what theoretical mathematicians say about it.