Methods for Solution of Nonlinear Operator Equations.

Intro -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.