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