Methods for Solution of Nonlinear Operator Equations

✍ Scribed by V. P. Tanana

• Publisher: De Gruyter
• Year: 2013
• Tongue: English
• Leaves: 248
• Series: Inverse and Ill-Posed Problems Series; 10
• Category: Library

✦ Table of Contents

Introduction
1 Regularization of nonlinear operator equations
§ 1.1 The basic definitions
§ 1.2 Setting of the problem and the regularization method
§ 1.3 The residual method
§ 1.4 Approximation of the regularized solution
2 Regularization of systems of nonlinear operator equations
§ 2.1 The basic definitions
§ 2.2 Setting of the problem and the regularization method
§ 2.3 The residual method
§ 2.4 Approximation of the regularized solution
§ 2.5 Regularization of the inverse filtration problem
3 T-regularization of nonlinear operator equations
§ 3.1 The basic definitions
§ 3.2 The T-regularization method
§ 3.3 The T-residual method
§ 3.4 Approximation of the T-regularized solution
4 Generalized regularization of nonlinear equations
§ 4.1 Convergence of the generalized regularization method when solving the equation with a. weakly-strongly closed operator
§ 4.2 The convergence of the residual method for equations with the weakly-strongly closed operator
§ 4.3 Approximation of the regularized solution. (The case of a weakly-strongly closed operator)
§ 4.4 The criterion of convergence of the generalized regularization method for solving nonlinear operator equations
§ 4.5 The convergence of the residual method for solving nonlinear equations
§ 4.6 The approximation of the regularized solution to an equation with an operator satisfying the condition (C)
5 The approximate regularization of nonlinear operator equations
§ 5.1 The basic definitions
§ 5.2 The convergence of the approximate regularization method
§ 5.3 Examples of operators
Bibliography