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| Author | : Curtis R. Vogel |
| Publisher | : SIAM |
| Total Pages | : 195 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898717574 |
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
| Author | : Albert Tarantola |
| Publisher | : SIAM |
| Total Pages | : 349 |
| Release | : 2005-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898717921 |
While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.
| Author | : Clive D. Rodgers |
| Publisher | : World Scientific |
| Total Pages | : 256 |
| Release | : 2000 |
| Genre | : Science |
| ISBN | : 981022740X |
Annotation Rodgers (U. of Oxford) provides graduate students and other researchers a background to the inverse problem and its solution, with applications relating to atmospheric measurements. He introduces the stages in the reverse order than the usual approach in order to develop the learner's intuition about the nature of the inverse problem. Annotation copyrighted by Book News, Inc., Portland, OR.
| Author | : Richard C. Aster |
| Publisher | : Elsevier |
| Total Pages | : 406 |
| Release | : 2018-10-16 |
| Genre | : Science |
| ISBN | : 0128134232 |
Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. - Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method - Includes an online instructor's guide that helps professors teach and customize exercises and select homework problems - Covers updated information on adjoint methods that are presented in an accessible manner
| Author | : Andreas Kirsch |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 314 |
| Release | : 2011-03-24 |
| Genre | : Mathematics |
| ISBN | : 1441984747 |
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.
| Author | : Michel Kern |
| Publisher | : John Wiley & Sons |
| Total Pages | : 232 |
| Release | : 2016-06-07 |
| Genre | : Mathematics |
| ISBN | : 1848218184 |
This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.
| Author | : Global Express Ltd. Co. |
| Publisher | : CRC Press |
| Total Pages | : 736 |
| Release | : 2000-03-21 |
| Genre | : Mathematics |
| ISBN | : 9780824719876 |
Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.
| Author | : Per Christian Hansen |
| Publisher | : SIAM |
| Total Pages | : 220 |
| Release | : 2010-01-01 |
| Genre | : Mathematics |
| ISBN | : 089871883X |
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
| Author | : Jari Kaipio |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 0387271325 |
This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.
| Author | : A.B. Bakushinsky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2007-09-28 |
| Genre | : Mathematics |
| ISBN | : 140203122X |
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.
