Regularization Algorithms for Ill-Posed Problems

Anatoly B. Bakushinsky

ISBN 10: 3110556308 / ISBN 13: 9783110556308

Published by De Gruyter Feb 2018, 2018

About this Item

Neuware - 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.

Seller Inventory # 9783110556308

Bibliographic Details

• Title: Regularization Algorithms for Ill-Posed Problems
• Publisher: De Gruyter Feb 2018
• Publication Date: 2018
• Language: English
• ISBN 10: 3110556308
• ISBN 13: 9783110556308
• Binding: Buch
• Condition: Neu
• Dimensions: 246W x 175H x 24D millimeters 246 millimeters width by 175 millimeters height by 24 millimeters depth
• Weight: 760 grams

About this title

Synopsis

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

About the Author

Anatoly B. Bakushinsky, Russian Academy of Sciences, Russia; Mihail M. Kokurin and Mihail Yu. Kokurin, Mari State University, Russia.