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ISBN:0123850487
Author: Clifford H. Thurber,Richard C. Aster
ISBN13: 978-0123850485
Title: Parameter Estimation and Inverse Problems
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Language: English
Category: Mathematics
Publisher: Academic Press; 2 edition (February 4, 2012)
Pages: 376

Parameter Estimation and Inverse Problems by Clifford H. Thurber,Richard C. Aster



Richard C. Aster, Clifford H. Thurber. p. cm. Includes bibliographical references and index. ISBN 978-0-12-385048-5 (hardback) 1. Parameter estimation. 2. Inverse problems (Differential equations) 3. Inversion (Geophysics) 4. Mathematical models. I. Thurber, Clifford H. II. Title. A central theme of this book is that continuous inverse problems can often be well-approximated by discrete inverse problems. We will generally refer to problems with small numbers of parameters as parameter estimation problems. Problems with a larger number of parameters, and which will often require the application of stabilizing constraints, will be referred to as inverse problems. examples of parameter estimation problems,. Example . A canonical parameter estimation problem is the fitting of a function, defined by a collection of parameters, to a data set.

This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors’ treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics.

Elsevier Academic Press, Amsterdam (2005). The two most common difficulties encountered in inverse modeling are nonuniqueness (multiple parameter sets represent the data equally well) and ill-posedness or illconditioning (small changes in the data result in large changes in the estimated parameters-the flip side of the smoothing characteristics of the forward model).

It promotes a fundamental understanding of parameter estimation and inverse problem philosophy and methodology. It introduces readers to Classical and Bayesian approaches to linear and nonlinear problems. The great strength of this book is that it is a 'one-shop-stop' for solving inverse problems; it contains many different methods for solving your particular problems and, in general, all of the background mathematics to help you understand the method itself. John Brittan, in THE LEADING EDGE, SEPT 2005. It is really a good book on inverse problems. And it is cool that they give you a disk with matlab functions, and the date for the examples. But I think that book is focus on the wrong things: some of the chapters could be removed, and some new chapters could be added.

Richard C. Aster, Brian Borchers, Clifford H.

Richard C. Aster, Brian Borchers, and Clifford Thurber1. 1c. 2002-2004, Aster, Borchers, and Thurber. This textbook evolved from a course in geophysical inverse methods taught dur-. ing the past decade at New Mexico Tech, first by Rick Aster and, for the last. Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model approaches that lie in the realm of inverse theory.

Author: Brian Borchers, Clifford H. Thurber, Richard C. Aster. Publisher: Academic Press. Publication Date: 2012-02-04.

Parameter Estimation and Inverse Problems, Second Edition provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors’ treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics.

Parameter Estimation and Inverse Problems, Second Edition introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject.

Includes appendices for review of needed concepts in linear, statistics, and vector calculus.Accessible to students and professionals without a highly specialized mathematical background.
Reviews: 6
Keth
This text was one of two books used for a graduate-level class iI attended for students of geophysics. The second textbook was Tarantola's.

Positive: The writing is very readable and the book is well organized. Prerequisite knowledge in statistics, linear algebra and vector calculus is summarised in appendices, which include exercises. The exercises throughout the book are well aligned with the difficulty level. Compared to Tarantola, the Aster et al. book is certainly more accessible for the novice, except for those with a background in pure mathematics. In addition to the exposition and exercises, the book also contains worked examples including, and this is a great plus, Matlab code that can be downloaded and run to follow along. The code is well written and comes with utility libraries that can then be used to work examples or even apply to research problems.

Neutral: The organisation of the material is very classical, starting with linear problems and treating non-linear problems. Some may prefer it this way. It happens that the class I attended used Aster et al. to cover the background material (ie, the appendices), then proceeded to general inverse problems through iterative methods using Tarantola, and finally returned to Aster to treat the linear case more in-depth. If I had to teach this class, I would probably do something similar and work through general, potentially non-linear problems before linear problems. The language and examples of Aster et al. are geared towards the seismologist or other solid-earth geophysicist, though there are some that allude to tomography.

Negative: The only potentially questionable choice is the total reliance on Matlab. I appreciate that this commercial software is widespread at least in US institutions, but the heavy use of custom-written Matlab code does reduce the usefulness of this book for those who don't have access to this programming environment.

I would give this text 4.5 points if I could. The 4-point score doesn't mean I'm not highly recommending it.
TheSuspect
I've spent the last year trying to teach myself inverse theory and wish I would have had this book from the beginning. Great explanations, logical progression of topics, good examples and sample MATLAB code. It has in my opinion the right amount of mathematical rigor for engineers and will get you going solving your own problems.
kewdiepie
This book strikes a good balance between applications and mathematical rigor. Useful for practitioners of numerical inversion as a reference and a gateway to the original mathematical works.
skyjettttt
The book arrived within the estimated delivery time and in excellent condition. Good introductory reference for the inverse problems theory and techniques. I recommend it.
Bladecliff
This book was required for my Inverse Theory class taught by Cliff Thurber, the 3rd author. Normally I don't like using the texts a professor has been a part of writing, but this text is very well written. It is easy to understand and gives many examples, which are nice when trying to do homework. The appendices also give a good background in information you will need to know for the class, which is much nicer than most texts that have no such information. Would suggest to anyone interested in parameter estimation.
Opithris
This is a comprehensive guide to understand the basic approaches to the inverse problems. As it addresses the Bayesian approaches as well toward the end of the text, one who is interested in parameter estimation should benefit from this book for further development and application of mathematical tools to deal with real life data from measurements or experiments.