Iterative Regularization Methods for Nonlinear Ill-Posed Problems PDF Download
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Author: Barbara Kaltenbacher
Publisher: Walter de Gruyter
ISBN: 311020827X
Category : Mathematics
Languages : en
Pages : 205
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Book Description
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.
Author: Barbara Kaltenbacher
Publisher: Walter de Gruyter
ISBN: 311020827X
Category : Mathematics
Languages : en
Pages : 205
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Book Description
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.
Author: Jennifer L. Mueller
Publisher: SIAM
ISBN: 1611972345
Category : Mathematics
Languages : en
Pages : 349
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Book Description
Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
Author: V.A. Morozov
Publisher: Springer Science & Business Media
ISBN: 1461252806
Category : Mathematics
Languages : en
Pages : 275
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Book Description
Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.
Author: Yakov Alber
Publisher: Springer Science & Business Media
ISBN: 1402043961
Category : Mathematics
Languages : en
Pages : 422
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Book Description
Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.
Author: A.N. Tikhonov
Publisher: Springer
ISBN: 9789401751698
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Author: Anatoly B. Bakushinsky
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110556383
Category : Mathematics
Languages : en
Pages : 447
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Book Description
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
Author: Anatoly B. Bakushinsky
Publisher: Walter de Gruyter
ISBN: 3110250659
Category : Mathematics
Languages : en
Pages : 153
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Book Description
Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.
Author: Yakov Alber
Publisher: Springer Science & Business Media
ISBN: 9781402043956
Category : Mathematics
Languages : en
Pages : 432
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Book Description
Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.
Author: Heinz W. Engl
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 592
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Book Description
Inverse and Ill-Posed Problems.
Author: A.N. Tikhonov
Publisher: Chapman and Hall/CRC
ISBN:
Category : Mathematics
Languages : en
Pages : 256
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Book Description
Professor A.N. Tikhonov was the founder of nonlinear ill-posed problem theory. This two-volume book introduces the reader to the theory and shows its applications in the natural sciences. The first volume introduces the foundations of the theory and provides the background necessary for the design of numerical methods. The second volume presents the finite-dimensional variants and modification of these methods to help readers use current computer software. It considers applications in linear algebra, vibrational spectroscopy, astrophysics, and medicine.
