Regularization Algorithms For Ill Posed Problems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Regularization Algorithms For Ill Posed Problems PDF full book. Access full book title Regularization Algorithms For Ill Posed Problems.
Author | : Anatoly B. Bakushinsky |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 342 |
Release | : 2018-02-05 |
Genre | : Mathematics |
ISBN | : 3110556383 |
Download Regularization Algorithms for Ill-Posed Problems Book in PDF, ePub and Kindle
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 | : A. Bakushinsky |
Publisher | : Springer Science & Business Media |
Total Pages | : 268 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401110263 |
Download Ill-Posed Problems: Theory and Applications Book in PDF, ePub and Kindle
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.
Author | : Shuai Lu |
Publisher | : ISSN |
Total Pages | : 0 |
Release | : 2013 |
Genre | : Numerical analysis |
ISBN | : 9783110286465 |
Download Regularization Theory for Ill-posed Problems Book in PDF, ePub and Kindle
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.
Author | : Barbara Kaltenbacher |
Publisher | : Walter de Gruyter |
Total Pages | : 205 |
Release | : 2008-09-25 |
Genre | : Mathematics |
ISBN | : 311020827X |
Download Iterative Regularization Methods for Nonlinear Ill-Posed Problems Book in PDF, ePub and Kindle
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 | : Shuai Lu |
Publisher | : Walter de Gruyter |
Total Pages | : 304 |
Release | : 2013-07-31 |
Genre | : Mathematics |
ISBN | : 3110286491 |
Download Regularization Theory for Ill-posed Problems Book in PDF, ePub and Kindle
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.
Author | : Anatoliĭ Borisovich Bakushinskiĭ |
Publisher | : |
Total Pages | : 323 |
Release | : 2018 |
Genre | : Differential equations, Partial |
ISBN | : 9783110557367 |
Download Regularization Algorithms for Ill-posed Problems Book in PDF, ePub and Kindle
Author | : Anatoly B. Bakushinsky |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 342 |
Release | : 2018-02-05 |
Genre | : Mathematics |
ISBN | : 3110557355 |
Download Regularization Algorithms for Ill-Posed Problems Book in PDF, ePub and Kindle
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. ContentsIntroductionRegularization Methods For Linear EquationsFinite Difference MethodsIterative Regularization MethodsFinite-Dimensional Iterative ProcessesVariational Inequalities and Optimization Problems
Author | : A.N. Tikhonov |
Publisher | : Springer Science & Business Media |
Total Pages | : 257 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 940158480X |
Download Numerical Methods for the Solution of Ill-Posed Problems Book in PDF, ePub and Kindle
Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Author | : Per Christian Hansen |
Publisher | : SIAM |
Total Pages | : 220 |
Release | : 2010-01-01 |
Genre | : Mathematics |
ISBN | : 089871883X |
Download Discrete Inverse Problems Book in PDF, ePub and Kindle
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
Author | : Otmar Scherzer |
Publisher | : Springer Science & Business Media |
Total Pages | : 1626 |
Release | : 2010-11-23 |
Genre | : Mathematics |
ISBN | : 0387929193 |
Download Handbook of Mathematical Methods in Imaging Book in PDF, ePub and Kindle
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.