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.