Methods for solving operator equations / V.P. Tanana.

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Bibliographic Details
Main Author:	Tanana, V. P. (Vitaliĭ Pavlovich)
Format:	eBook
Language:	English
Published:	[Place of publication not identified] : [De Gruyter], [2012]
Edition:	[Digital ed.].
Series:	Inverse and ill-posed problems series.
Subjects:	Operator equations > Numerical solutions. Numerical analysis. MATHEMATICS > Functional Analysis. Numerical analysis Operator equations > Numerical solutions
Online Access:	Click for online access

Table of Contents:

Preface
Introduction
1 Regularization of linear operator equations.
Â1.1 Classification of ill-posed problems and the concept of the optimal method
Â1.2 The estimate from below for Î?opt
Â1.3 The error of the regularization method
Â1.4 The algorithmic peculiarities of the generalized residual principle
Â1.5 The error of the quasi-solutions method
Â1.6 The regularization method with the parameter Î± chosen by the residual
Â1.7 The projection regularization method
Â1.8 On the choice of the optimal regularization parameter
Â1.9 Optimal methods for solving unstable problems with additional information on the operator AÂ1.10 On the regularization of operator equations of the first kind with the approximately given operator and on the choice of the regularization parameter
Â1.11 The generalized residual principle
Â1.12 The optimum of the generalized residual principle
2 Finite â€? dimensional methods of constructing regularized solutions
Â2.1 The notion of Ï?-uniform convergence of linear operators
Â2.2 The general scheme of finite-dimensional approximation in the regularization methodÂ2.3 Application of the general scheme to the projection and finite difference methods
Â2.4 The general scheme of finite-dimensional approximation in the generalized residual method
Â2.5 The iterative method for determining the finite-dimensional approximation in the generalized residual principle
Â2.6 The general scheme of finite-dimensional approximations in the quasi-solution method
Â2.7 The necessary and sufficient conditions for the convergence of finite-dimensional approximations in the regularization methodÂ2.8 On the discretization the ofvariational problem (1.11.5)
Â2.9 Finite-dimensional approximation of regularized solutions
Â2.10 Application
3 Regularization of nonlinear operator equations
Â3.1 Approximate solution of nonlinear operator equations with a disturbed operator by the regularization method.
Â3.2 Approximate solution of implicit operator equations of the first kind by the regularization method

Methods for solving operator equations / V.P. Tanana.

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