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Iterative Regularization Methods for Nonlinear Ill-Posed Problems

2008-09-25 Mathematics
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Release : 2008-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 27X/5 ( reviews)

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Book Synopsis Iterative Regularization Methods for Nonlinear Ill-Posed Problems by : Barbara Kaltenbacher

Download or read book Iterative Regularization Methods for Nonlinear Ill-Posed Problems written by Barbara Kaltenbacher. This book was released on 2008-09-25. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

Regularization Algorithms for Ill-Posed Problems

2018-02-05 Mathematics
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Release : 2018-02-05
Genre : Mathematics
Kind : eBook
Book Rating : 383/5 ( reviews)

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Book Synopsis Regularization Algorithms for Ill-Posed Problems by : Anatoly B. Bakushinsky

Download or read book Regularization Algorithms for Ill-Posed Problems written by Anatoly B. Bakushinsky. This book was released on 2018-02-05. Available in PDF, EPUB and Kindle. Book excerpt: This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems

Ill-Posed Problems: Theory and Applications

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 263/5 ( reviews)

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Book Synopsis Ill-Posed Problems: Theory and Applications by : A. Bakushinsky

Download or read book Ill-Posed Problems: Theory and Applications written by A. Bakushinsky. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have been characterized by the increasing amountofpublications in the field ofso-called ill-posed problems. This is easilyunderstandable because we observe the rapid progress of a relatively young branch ofmathematics, ofwhich the first results date back to about 30 years ago. By now, impressive results have been achieved both in the theory ofsolving ill-posed problems and in the applicationsofalgorithms using modem computers. To mention just one field, one can name the computer tomography which could not possibly have been developed without modem tools for solving ill-posed problems. When writing this book, the authors tried to define the place and role of ill posed problems in modem mathematics. In a few words, we define the theory of ill-posed problems as the theory of approximating functions with approximately given arguments in functional spaces. The difference between well-posed and ill posed problems is concerned with the fact that the latter are associated with discontinuous functions. This approach is followed by the authors throughout the whole book. We hope that the theoretical results will be of interest to researchers working in approximation theory and functional analysis. As for particular algorithms for solving ill-posed problems, the authors paid general attention to the principles ofconstructing such algorithms as the methods for approximating discontinuous functions with approximately specified arguments. In this way it proved possible to define the limits of applicability of regularization techniques.

Regularization Methods for Ill-Posed Optimal Control Problems

2018-10-04 Mathematics
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Release : 2018-10-04
Genre : Mathematics
Kind : eBook
Book Rating : 861/5 ( reviews)

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Book Synopsis Regularization Methods for Ill-Posed Optimal Control Problems by : Frank Pörner

Download or read book Regularization Methods for Ill-Posed Optimal Control Problems written by Frank Pörner. This book was released on 2018-10-04. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed optimization problems appear in a wide range of mathematical applications, and their numerical solution requires the use of appropriate regularization techniques. In order to understand these techniques, a thorough analysis is inevitable. The main subject of this book are quadratic optimal control problems subject to elliptic linear or semi-linear partial differential equations. Depending on the structure of the differential equation, different regularization techniques are employed, and their analysis leads to novel results such as rate of convergence estimates.

Regularization of Inverse Problems

2000-03-31 Mathematics
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Release : 2000-03-31
Genre : Mathematics
Kind : eBook
Book Rating : 404/5 ( reviews)

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Book Synopsis Regularization of Inverse Problems by : Heinz Werner Engl

Download or read book Regularization of Inverse Problems written by Heinz Werner Engl. This book was released on 2000-03-31. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates.

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