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Author : Marcel Rennoch
Release : 2017
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Regularization Methods in Banach Spaces Applied to Inverse Medium Scattering Problems by : Marcel Rennoch
Download or read book Regularization Methods in Banach Spaces Applied to Inverse Medium Scattering Problems written by Marcel Rennoch. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas Schuster
Release : 2012-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 723/5 ( reviews)
Book Synopsis Regularization Methods in Banach Spaces by : Thomas Schuster
Download or read book Regularization Methods in Banach Spaces written by Thomas Schuster. This book was released on 2012-07-30. Available in PDF, EPUB and Kindle. Book excerpt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
Author : Barbara Kaltenbacher
Release : 2008-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 27X/5 ( reviews)
Book Synopsis Iterative Regularization Methods for Nonlinear Ill-Posed Problems by : Barbara Kaltenbacher
Download or read book Iterative Regularization Methods for Nonlinear Ill-Posed Problems written by Barbara Kaltenbacher. This book was released on 2008-09-25. 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.
Author :
Release : 2013-11-22
Genre : Technology & Engineering
Kind : eBook
Book Rating : 343/5 ( reviews)
Book Synopsis Regularization for Applied Inverse and Ill-Posed Problems by :
Download or read book Regularization for Applied Inverse and Ill-Posed Problems written by . This book was released on 2013-11-22. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Anatoly B. Bakushinsky
Release : 2018-02-05
Genre : Mathematics
Kind : eBook
Book Rating : 383/5 ( reviews)
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. This book was released on 2018-02-05. 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
