Description

Book 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

Regularization Algorithms for Ill-Posed Problems

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    A Hardback by Anatoly B. Bakushinsky, Mikhail M. Kokurin, Mikhail Yu. Kokurin

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      Book details

      Publisher De Gruyter
      Published 5 February 2018
      ISBN-13 9783110556308
      978-3110556308
      ISBN-10 3110556308
      Also in:
      Applied mathematics Calculus and mathematical analysis Functional analysis and transforms

      Description

      Book 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

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