Download or read book Iterative Regularization Methods for Nonlinear Ill Posed Problems written by Barbara Kaltenbacher and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 205 pages. 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.
Download or read book Nonlinear Ill Posed Problems written by A.N. Tikhonov and published by Springer. This book was released on 1997-12-15 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Ill posed Problems written by Andreĭ Nikolaevich Tikhonov and published by . This book was released on 1998 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Ill posed Problems written by Andreĭ Nikolaevich Tikhonov and published by Springer. This book was released on 1998 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Ill posed Problems of Monotone Type written by Yakov Alber and published by Springer Science & Business Media. This book was released on 2006-02-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear and Nonlinear Inverse Problems with Practical Applications written by Jennifer L. Mueller and published by SIAM. This book was released on 2012-11-30 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Methods for Solving Incorrectly Posed Problems written by V.A. Morozov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Ill posed Problems of Monotone Type written by Yakov Alber and published by Springer Science & Business Media. This book was released on 2006-02-23 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Iterative Methods for Ill Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter. This book was released on 2010-12-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 342 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
Download or read book Nonlinear ill posed problems written by Andrej N. Tichonov and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Surveys on Solution Methods for Inverse Problems written by David Colton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Science & Business Media. This book was released on 2011-03-24 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
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 2000-03-31 with total page 340 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.
Download or read book Iterative Methods for Nonlinear Ill Posed Problems written by Atef Ibrahim Elmahdy and published by LAP Lambert Academic Publishing. This book was released on 2012-04 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation of the form F(x) = y, where F is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not be often possible or may not be worth looking for due to physical constraints. In such situation, it is desirable to know how the so-called approximate solution approximates the exact solution, and what would be the error involved in such procedures. The main focus of the book is on the study of stably solving nonlinear ill posed operator equations of the form F(x)=y, with monotone nonlinear operator F in an infinite dimensional real Hilbert space X, that is , F obeys the monotonicity property. It is assumed that the exact data y is unknown and usually only noisy data are available. Problems of this type arise in a number of applications. Since the solution does not depend continuously on the data, the ill-posed problem has to be regularized. We considered iterative methods which converge to the unique solution of the method of Lavrentiev regularization.
Download or read book Nonlinear Ill Posed Problems written by A.N. Tikhonov and published by Chapman and Hall/CRC. This book was released on 1998 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
