Iterative Fejér Processes in Ill-Posed Problems

A brief survey is given concerning iterative processes of Fejér type for basic statements of ill-posed problems, including constrained quadratic and convex minimization problems, variational inequalities, and linear and nonlinear operator equations in Hilbert spaces. By applying the method of succes...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2020-06, Vol.60 (6), p.938-949
Main Author: Vasin, V. V.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Fixed points (mathematics)
Hilbert space
Ill posed problems
Mathematics
Mathematics and Statistics
Nonlinear equations
Operators
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Summary:A brief survey is given concerning iterative processes of Fejér type for basic statements of ill-posed problems, including constrained quadratic and convex minimization problems, variational inequalities, and linear and nonlinear operator equations in Hilbert spaces. By applying the method of successive approximations and its modification using correction factors, all these statements reduce to the problem of finding fixed points of nonexpansive Fejér operators. Material is also presented related to a two-stage method of constructing a regularizing algorithm for nonlinear ill-posed problems with monotone operators. An economic way is described by which the algorithm takes into account additional a priori information on the solution using Fejér maps.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542520060111