A method to obtain the best uniform polynomial approximation for the family of rational function

Subject Areas : Numerical Analysis

M. A. Fariborzi Araghi ¹ , F. Foroozanfar ²

1 - Department of Mathematics, Islamic Azad university, Central Tehran branch
2 - Ms.student of Mathematics, Islamic Azad university, Kermanshah branch, Kermanshah, Iran

Received: 2014-09-20 Accepted : 2014-11-20 Published : 2015-01-01

Keywords: uniform norm, the best uniform polynomial approximation, alternating set, Chebyshev’s polynomials, Chebyshev’s expansion,

Abstract :

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1for both cases b2-4ac L 0and b2-4ac G 0.

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