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Necessary And Sufficient Conditions For Convergence Of Regularization Methods For Solving Linear Operator Equations Of The First Kind
Download Necessary And Sufficient Conditions For Convergence Of Regularization Methods For Solving Linear Operator Equations Of The First Kind full books in PDF, epub, and Kindle. Read online Necessary And Sufficient Conditions For Convergence Of Regularization Methods For Solving Linear Operator Equations Of The First Kind ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Regularization of Inverse Problems by : Heinz Werner Engl
Download or read book Regularization of Inverse Problems written by Heinz Werner Engl and published by Springer Science & Business Media. This book was released on 1996-07-31 with total page 348 pages. 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.
Book Synopsis An Introduction to the Mathematical Theory of Inverse Problems by : Andreas Kirsch
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Nature. This book was released on 2021-02-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
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 and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 447 pages. 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
Book Synopsis Improperly Posed Problems and Their Numerical Treatment by : Prof. Dr. G. Hämmerlin
Download or read book Improperly Posed Problems and Their Numerical Treatment written by Prof. Dr. G. Hämmerlin and published by Birkhäuser. This book was released on 2013-11-21 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whilst improperly posed problems appear in several branches of applied and pure mathematics, this conference concentrated mainly on the practical treatment of ill posedness. The participants came from 12 countries. The interchange of ideas reflected the spectrum of questions arising in connection with the subject of the conference, where currently progresses in research are made. This volume contains 17 papers presented at the con ference. Focal points in the programme were: Problems of regularisation, parameter identification, free boundary and inverse problems in differential equations and inte gral equations of the first kind. Problems, which appear in science, in technical fields and in medicine are dis cussed as well as general operator equations. In a jOint discussion, several open problems have been worked out which are collected at the end of the volume. The editor's thanks go to all contributors and parti cipants who made the conference a success; to the manage ment of the institute with its unique atmosphere; to the Birkhauser Verlag for the possibility to publish the vo lume in the well-known ISNM series; to Dr. P. Jochum (Mlin chen) for assistance in organization and to Mrs. Chr. Rogg (Augsburg) for her excellent typing of several manuscripts.
Book Synopsis Constructive Methods for the Practical Treatment of Integral Equations by : G. Hämmerlin
Download or read book Constructive Methods for the Practical Treatment of Integral Equations written by G. Hämmerlin and published by Birkhäuser. This book was released on 2013-03-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: O I 1 -1 durch die GauB-Quadraturformel Q I n n L w 0 f (x 0) - i=1 1 1 Sei Rn : = I - Q das Fehlerfunktional. n Izl1, Fur eine im Kreis Kr I Kr : = {z E a: holomorphe Funktion f, f(z) = L i=O sei f i i - = x . (1. 1) : = sup{ I a 0 I r i E:JN und R (qo) * O}, qo (x) o 1 n 1 1 In Xr := {f: f holomorph in Kr und Iflr
Book Synopsis Optimal Methods for Ill-Posed Problems by : Vitalii P. Tanana
Download or read book Optimal Methods for Ill-Posed Problems written by Vitalii P. Tanana and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-03-19 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems
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 and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 268 pages. 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.
Book Synopsis Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) by : Heinrich G W Begehr
Download or read book Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) written by Heinrich G W Begehr and published by World Scientific. This book was released on 2003-08-04 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
Book Synopsis Theory of Linear Ill-Posed Problems and its Applications by : Valentin K. Ivanov
Download or read book Theory of Linear Ill-Posed Problems and its Applications written by Valentin K. Ivanov and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a revised and extended version of the Russian edition from 1978. It includes the general theory of linear ill-posed problems concerning e. g. the structure of sets of uniform regularization, the theory of error estimation, and the optimality method. As a distinguishing feature the book considers ill-posed problems not only in Hilbert but also in Banach spaces. It is natural that since the appearance of the first edition considerable progress has been made in the theory of inverse and ill-posed problems as wall as in ist applications. To reflect these accomplishments the authors included additional material e. g. comments to each chapter and a list of monographs with annotations.
Book Synopsis The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind by : C. W. Groetsch
Download or read book The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind written by C. W. Groetsch and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for Approximate Solution of Inverse Problems by : A.B. Bakushinsky
Download or read book Iterative Methods for Approximate Solution of Inverse Problems written by A.B. Bakushinsky and published by Springer Science & Business Media. This book was released on 2007-09-28 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Regularization for Applied Inverse and Ill-Posed Problems by : Bernd Hofmann
Download or read book Regularization for Applied Inverse and Ill-Posed Problems written by Bernd Hofmann and published by Springer. This book was released on 1986-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ill-Posed Problems with A Priori Information by : V. V. Vasin
Download or read book Ill-Posed Problems with A Priori Information written by V. V. Vasin and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
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 and published by BoD – Books on Demand. This book was released on 2018-10-04 with total page 181 pages. 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.
Book Synopsis Stability Estimates and Regularization for an Inverse Heat Conduction Problem by : Heinz W. Engl
Download or read book Stability Estimates and Regularization for an Inverse Heat Conduction Problem written by Heinz W. Engl and published by . This book was released on 1987 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods for Solution of Nonlinear Operator Equations by : V. P. Tanana
Download or read book Methods for Solution of Nonlinear Operator Equations written by V. P. Tanana and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Book Synopsis Reviews in Operator Theory, 1980-86 by : American Mathematical Society
Download or read book Reviews in Operator Theory, 1980-86 written by American Mathematical Society and published by . This book was released on 1989 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:
