Regularization Algorithms for Ill-Posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularization Algorithms for Ill-Posed Problems write by Anatoly B. Bakushinsky. This book was released on 2018-02-05. Regularization Algorithms for Ill-Posed Problems available 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
Ill-Posed Problems: Theory and Applications
Ill-Posed Problems: Theory and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ill-Posed Problems: Theory and Applications write by A. Bakushinsky. This book was released on 2012-12-06. Ill-Posed Problems: Theory and Applications available 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.
Regularization Theory for Ill-posed Problems
Regularization Theory for Ill-posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularization Theory for Ill-posed Problems write by Shuai Lu. This book was released on 2013-07-31. Regularization Theory for Ill-posed Problems available 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.
Regularization Algorithms for Ill-posed Problems
Regularization Algorithms for Ill-posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularization Algorithms for Ill-posed Problems write by Anatoliĭ Borisovich Bakushinskiĭ. This book was released on 2018. Regularization Algorithms for Ill-posed Problems available in PDF, EPUB and Kindle.
Iterative Regularization Methods for Nonlinear Ill-Posed Problems
Iterative Regularization Methods for Nonlinear Ill-Posed Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Iterative Regularization Methods for Nonlinear Ill-Posed Problems write by Barbara Kaltenbacher. This book was released on 2008-09-25. Iterative Regularization Methods for Nonlinear Ill-Posed Problems available 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.
