Best uniform polynomial approximation of some rational functions

✍ Scribed by Mehdi Dehghan; M.R. Eslahchi

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 637 KB
• Volume: 59
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.07.016

✦ Synopsis

In this research paper using the Chebyshev expansion, we explicitly determine the best uniform polynomial approximation out of P qn (the space of polynomials of degree at most qn) to a class of rational functions of the form 1/(T q (a) ± T q (x)) on [-1, 1], where T q (x) is the first kind of Chebyshev polynomial of degree q and a 2 > 1. 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.