A method to obtain the best uniform polynomial
approximation for the family of rational
function
c bx ax
2
1
M. A. Fariborzi Araghi
1
,F. Froozanfar
2
1
Department of Mathematics, Islamic Azad university, Central Tehran branch,
P.O.Box 13.185.768, Tehran, Iran.
2
Ms.student of Mathematics, Islamic Azad university, Kermanshah branch
, Kermanshah, Iran
*Correspondence E‐mail: M. A. Fariborzi Araghi: fariborzi.araghi@gmail.com
© 2015 Copyright by Islamic Azad University, Rasht Branch, Rasht, Iran
Online version is available on: www.ijo.iaurasht.ac.ir
Abstract
In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion,
we obtain the best uniform polynomial approximation out of
n
P
2
to a class of
rational functions of theform
1
2
c ax on any non symmetric interval e d , .
Using the obtained approximation, we provide the best uniform polynomial
approximation to a class of rational functions of the form
1
2
c bx ax for
both cases 0 4
2
ac b and 0 4
2
ac b .
Key words: Chebyshev’s polynomials, Chebyshev’s expansion, uniform norm,
the best uniform polynomial approximation, alternating set.
1. Introduction
.
cos 2 1
sin sin cos cos cos cos 1
2
1
0
p t t
p pn t p pn t pn t p t
x T t b
p p
n pn n pn pn p n
j
pj
pj
In
section 2, we characterize the best On of the important and applicable subjects in
applied mathematics is the best approximation for functions. A large number of
paper and books have considered this problem in various points of view.
Volume 7, issue 1, Winter 2015, 753-766
Research Paper