Best uniform polynomial approximation of some rational functions

Best uniform polynomial approximation of some rational functions

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Article ID: iaor20122331
Volume: 59
Issue: 1
Start Page Number: 382
End Page Number: 390
Publication Date: Jan 2010
Journal: Computers and Mathematics with Applications
Authors: ,
Keywords: approximation, Chebyshev
Abstract:

In this research paper using the Chebyshev expansion, we explicitly determine the best uniform polynomial approximation out of P q n equ1 (the space of polynomials of degree at most q n equ2) to a class of rational functions of the form 1 / ( T q ( a ) ± T q ( x ) ) equ3 on [ 1 , 1 ] equ4, where T q ( x ) equ5 is the first kind of Chebyshev polynomial of degree q equ6 and a 2 > 1 equ7. In this way we give some new theorems about the best approximation of this class of rational functions. Furthermore we obtain the alternating set of this class of functions.

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