Algorithm for Constructing the Chebyshev-Type Polynomials and the Chebyshev-Type Approximations with a Given Weight

The polynomials which give the minimum for the minimax norm are very useful in practical applications of various numerical algorithms. However, except the well-known Chebyshev's polynomials of first and second order there are no such polynomials specified in an explicit algebraic form. The pape...

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Published in2022 International Conference on Electrical Engineering and Photonics (EExPolytech) pp. 143 - 145
Main Authors Berdnikov, Alexander, Solovyev, Konstantin, Krasnova, Nadezhda, Golovitski, Alexander, Syasko, Mikhail
Format Conference Proceeding
LanguageEnglish
Published IEEE 20.10.2022
Subjects
Approximation algorithms
Chebyshev approximation
Chebyshev polynomials
Electrical engineering
minimax norm
optimal approximation
Photonics
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Summary:The polynomials which give the minimum for the minimax norm are very useful in practical applications of various numerical algorithms. However, except the well-known Chebyshev's polynomials of first and second order there are no such polynomials specified in an explicit algebraic form. The paper considers the numerical algorithm(s) to generate the coefficients of the polynomials which: a) produce an optimal approximation for a given function in a minimax norm with some weight, b) produce an optimal deviation from zero with some weight and with a fixed high order coefficient.
ISSN:2771-697X
DOI:10.1109/EExPolytech56308.2022.9950861