On the Achievable Level of Accuracy for the Solution of Abstract Ill-Posed Problems and Nonlinear Operator Equations in a Banach Space

It has been shown that, for a wide class of ill–posed problems of finding the value of a discontinuous operator by an approximately specified element in a Banach space, the level of accuracy for the resulting solution cannot be higher in order than the level of error in input data. A similar result...

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Bibliographic Details
Published in:Russian mathematics Vol. 66; no. 3; pp. 16 - 21
Main Authors: Kokurin, M. Yu, Bakushinsky, A. B.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.03.2022
Springer Nature B.V
Subjects:
Banach spaces
Ill posed problems
Mathematical analysis
Mathematics
Mathematics and Statistics
operator equation
accuracy estimate
Banach space
ill-posed problem
ISSN:1066-369X, 1934-810X
Online Access:Get full text
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Summary:It has been shown that, for a wide class of ill–posed problems of finding the value of a discontinuous operator by an approximately specified element in a Banach space, the level of accuracy for the resulting solution cannot be higher in order than the level of error in input data. A similar result is established for a class of nonlinear operator equations with an approximate right side. The classes of problems for which these orders are coincident are specified.
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ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X22030057