Regularization Algorithms for Ill-Posed Problems / / Anatoly B. Bakushinsky, Mikhail M. Kokurin, Mikhail Yu. Kokurin.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2018 Part 1
• VerfasserIn: Bakushinsky, Anatoly B.,; Kokurin, Mikhail M.,; Kokurin, Mikhail Yu.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2018]; ©2018
• Year of Publication: 2018
• Language: English
• Series: Inverse and Ill-Posed Problems Series , 61
• Physical Description: 1 online resource (XVI, 326 p.)

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

Table of Contents

Frontmatter -- Preface -- Contents -- 1 Introduction -- 2 Regularization Methods For Linear Equations -- 3 Regularization of Ill-Posed Cauchy Problems by Finite Difference Methods -- 4 Iterative Regularization Methods For Nonlinear Equations -- 5 Finite-Dimensional Iterative Processes for Irregular Nonlinear Equations -- 6 Regularization of Nonlinear Variational Inequalities and Optimization Problems -- Bibliography -- Index