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Methods for Solving Operator Equations.

By: Series: Inverse and Ill-Posed Problems SerPublisher: Berlin/Boston : De Gruyter, Inc., 1997Copyright date: ©1997Description: 1 online resource (223 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110900156
Subject(s): Genre/Form: Additional physical formats: Print version:: Methods for Solving Operator EquationsDDC classification:
  • 515.724
LOC classification:
  • QA329 -- .T36 1997eb
Online resources:
Contents:
Intro -- Preface -- Introduction -- 1 Regularization of linear operator equations. -- 1.1 Classification of ill-posed problems and the concept of the optimal method -- 1.2 The estimate from below for Δopt -- 1.3 The error of the regularization method -- 1.4 The algorithmic peculiarities of the generalized residual principle -- 1.5 The error of the quasi-solutions method -- 1.6 The regularization method with the parameter α chosen by the residual -- 1.7 The projection regularization method -- 1.8 On the choice of the optimal regularization parameter -- 1.9 Optimal methods for solving unstable problems with additional information on the operator A -- 1.10 On the regularization of operator equations of the first kind with the approximately given operator and on the choice of the regularization parameter -- 1.11 The generalized residual principle -- 1.12 The optimum of the generalized residual principle -- 2 Finite - dimensional methods of constructing regularized solutions -- 2.1 The notion of τ-uniform convergence of linear operators -- 2.2 The general scheme of finite-dimensional approximation in the regularization method -- 2.3 Application of the general scheme to the projection and finite difference methods -- 2.4 The general scheme of finite-dimensional approximation in the generalized residual method -- 2.5 The iterative method for determining the finite-dimensional approximation in the generalized residual principle -- 2.6 The general scheme of finite-dimensional approximations in the quasi-solution method -- 2.7 The necessary and sufficient conditions for the convergence of finite-dimensional approximations in the regularization method -- 2.8 On the discretization the ofvariational problem (1.11.5) -- 2.9 Finite-dimensional approximation of regularized solutions -- 2.10 Application.
3 Regularization of nonlinear operator equations -- 3.1 Approximate solution of nonlinear operator equations with a disturbed operator by the regularization method. -- 3.2 Approximate solution of implicit operator equations of the first kind by the regularization method -- 3.3 Optimal by the order method for solving nonlinear unstable problems -- Bibliography.
Summary: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan Available EBKAF-N00019266
Ebrary Ebrary Algeria Available
Ebrary Ebrary Cyprus Available
Ebrary Ebrary Egypt Available
Ebrary Ebrary Libya Available
Ebrary Ebrary Morocco Available
Ebrary Ebrary Nepal Available EBKNP-N00019266
Ebrary Ebrary Sudan Available
Ebrary Ebrary Tunisia Available
Total holds: 0

Intro -- Preface -- Introduction -- 1 Regularization of linear operator equations. -- 1.1 Classification of ill-posed problems and the concept of the optimal method -- 1.2 The estimate from below for Δopt -- 1.3 The error of the regularization method -- 1.4 The algorithmic peculiarities of the generalized residual principle -- 1.5 The error of the quasi-solutions method -- 1.6 The regularization method with the parameter α chosen by the residual -- 1.7 The projection regularization method -- 1.8 On the choice of the optimal regularization parameter -- 1.9 Optimal methods for solving unstable problems with additional information on the operator A -- 1.10 On the regularization of operator equations of the first kind with the approximately given operator and on the choice of the regularization parameter -- 1.11 The generalized residual principle -- 1.12 The optimum of the generalized residual principle -- 2 Finite - dimensional methods of constructing regularized solutions -- 2.1 The notion of τ-uniform convergence of linear operators -- 2.2 The general scheme of finite-dimensional approximation in the regularization method -- 2.3 Application of the general scheme to the projection and finite difference methods -- 2.4 The general scheme of finite-dimensional approximation in the generalized residual method -- 2.5 The iterative method for determining the finite-dimensional approximation in the generalized residual principle -- 2.6 The general scheme of finite-dimensional approximations in the quasi-solution method -- 2.7 The necessary and sufficient conditions for the convergence of finite-dimensional approximations in the regularization method -- 2.8 On the discretization the ofvariational problem (1.11.5) -- 2.9 Finite-dimensional approximation of regularized solutions -- 2.10 Application.

3 Regularization of nonlinear operator equations -- 3.1 Approximate solution of nonlinear operator equations with a disturbed operator by the regularization method. -- 3.2 Approximate solution of implicit operator equations of the first kind by the regularization method -- 3.3 Optimal by the order method for solving nonlinear unstable problems -- Bibliography.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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