Improved Accuracy Estimation of the Tikhonov Method for Ill-Posed Optimization Problems in Hilbert Space

The Tikhonov method is studied as applied to ill-posed problems of minimizing a smooth nonconvex functional. Assuming that the sought solution satisfies the source condition, an accuracy estimate for the Tikhonov method is obtained in terms of the regularization parameter. Previously, such an estima...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics Vol. 63; no. 4; pp. 519 - 527
Main Author: Kokurin, M. M.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.04.2023
Springer Nature B.V
Subjects:
Accuracy
Approximation
Computational Mathematics and Numerical Analysis
Estimates
General Numerical Methods
Hilbert space
Ill posed problems
Inequality
Mathematics
Mathematics and Statistics
Optimization
Regularization
Regularization methods
ill-posed optimization problem in Hilbert space
Tikhonov method
accuracy estimation
ISSN:0965-5425, 1555-6662
Online Access:Get full text
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Summary:The Tikhonov method is studied as applied to ill-posed problems of minimizing a smooth nonconvex functional. Assuming that the sought solution satisfies the source condition, an accuracy estimate for the Tikhonov method is obtained in terms of the regularization parameter. Previously, such an estimate was obtained only under the assumption that the functional is convex or under a structural condition imposed on its nonlinearity. Additionally, a new accuracy estimate for the Tikhonov method is obtained in the case of an approximately specified functional.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542523040103