Estimates for Best Approximation to Rational Functions

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

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)-1 on 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)-1 for both cases b2-4a...

Best uniform approximation to a class of rational functions

The best uniform polynomial approximation of two classes of rational functions

In this paper we obtain the explicit form of the best uniform polynomial approximations out of Pn of two classes of rational functions using properties of Chebyshev polynomials. In this way we present some new theorems and lemmas. Some examples will be given to support the results.

Best Simultaneous Approximation on Small Regions by Rational Functions

We study the behavior of best simultaneous (lq , Lp)-approximation by rational functions on an interval, when the measure tends to zero. In addition, we consider the case of polynomial approximation on a finite union of intervals. We also get an interpolation result.

Best uniform polynomial approximation of some rational functions

This thesis is based on the following paper :Mehdi Dehghan , M.R. Eslahchi, Best uniform polynomialapproximation of some rational functions , Computers andMathematics with Applications ,Best polynomial approximation problem is one of the mostimportant and applicable subjects in the approxi References1. [1] J . C . Mason , D . C . Handscomb , Chebyshevpolynomials ...