Optimization Properties of Generalized Chebyshev–Poisson Integrals

Chebyshev polynomials of the first kind are applied to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on an interval is solved, and its approximate properties on Holder classes H 1 ar...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2024-07, Vol.60 (4), p.613-620
Main Authors: Mishchuk, A. Yu, Shutovskyi, A. M.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Chebyshev approximation
Control
Functionals
Mathematics
Mathematics and Statistics
Operators (mathematics)
Optimization
Polynomials
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
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Summary:Chebyshev polynomials of the first kind are applied to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on an interval is solved, and its approximate properties on Holder classes H 1 are analyzed. An exact equality is obtained for the deviation of Hölder class functions from the generalized Chebyshev–Poisson integral.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-024-00700-8