Regularization For Applied Inverse And Ill Posed Problems
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Regularization For Applied Inverse And Ill Posed Problems
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Author :
language : de
Publisher: Springer-Verlag
Release Date : 2013-11-22
Regularization For Applied Inverse And Ill Posed Problems written by and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Technology & Engineering categories.
Iterative Regularization Methods For Nonlinear Ill Posed Problems
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Author : Barbara Kaltenbacher
language : en
Publisher: Walter de Gruyter
Release Date : 2008-09-25
Iterative Regularization Methods For Nonlinear Ill Posed Problems written by Barbara Kaltenbacher and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-25 with Mathematics categories.
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
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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Regularization Algorithms For Ill Posed Problems written by Anatoly B. Bakushinsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
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
Nonlinear Ill Posed Problems
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Author : Andreĭ Nikolaevich Tikhonov
language : en
Publisher:
Release Date : 1998
Nonlinear Ill Posed Problems written by Andreĭ Nikolaevich Tikhonov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Differential equations, Nonlinear categories.
Regularization Theory For Ill Posed Problems
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Author : Shuai Lu
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31
Regularization Theory For Ill Posed Problems written by Shuai Lu and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.
This monograph is a valuable contribution to the highly topical and extremly productive field of regularisation methods for inverse and ill-posed problems. The author is an internationally outstanding and accepted mathematician in this field. In his book he offers a well-balanced mixture of basic and innovative aspects. He demonstrates new, differentiated viewpoints, and important examples for applications. The book demontrates the current developments in the field of regularization theory, such as multiparameter regularization and regularization in learning theory. The book is written for graduate and PhD students and researchers in mathematics, natural sciences, engeneering, and medicine.
Regularization Of Inverse Problems
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Author : Heinz Werner Engl
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-03-31
Regularization Of Inverse Problems written by Heinz Werner Engl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-31 with Mathematics categories.
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.
Iterative Methods For Ill Posed Problems
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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter
Release Date : 2011
Iterative Methods For Ill Posed Problems written by Anatoly B. Bakushinsky and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization
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Author : Jens Flemming
language : en
Publisher: Springer
Release Date : 2018-09-08
Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization written by Jens Flemming and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.
Well Posed Ill Posed And Intermediate Problems With Applications
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Author : Petrov Yuri P.
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Well Posed Ill Posed And Intermediate Problems With Applications written by Petrov Yuri P. and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.
Computational Methods For Applied Inverse Problems
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Author : Yanfei Wang
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-30
Computational Methods For Applied Inverse Problems written by Yanfei Wang and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.