149 articles – 164 Notices  [english version]

inria-00201893, version 1

Best uniform approximation to a class of rational functions

Zhitong Zheng 1, Jun-Hai Yong 2

Journal of Mathematical Analysis and applications 334 (2007) 909-921

Résumé : We explicitly determine the best uniform polynomial approximation p∗n−1 to a class of rational functions of the form 1/(x − c)2 + K(a,b, c,n)/(x − c) on [a, b] represented by their Chebyshev expansion, where a, b, and c are real numbers, n − 1 denotes the degree of the best approximating polynomial, and K is a constant determined by a, b, c, and n. Our result is based on the explicit determination of a phase angle η in the representation of the approximation error by a trigonometric function. Moreover, we formulate an ansatz which offers a heuristic strategies to determine the best approximating polynomial to a function represented by its Chebyshev expansion. Combined with the phase angle method, this ansatz can be used to find the best uniform approximation to some more functions. © 2006 Elsevier Inc. All rights reserved.

  • 1 :  School of Software (THSS)
  • Tsinghua University
  • 2 :  CAD (CAD LIAMA INRIA Paris - Rocquencourt)
  • Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] – CNRS – Institut national de la recherche agronomique (INRA) – Chinese Academy of Science (CAS) – Institute of Automation, Chinese Academy of Sciences – INRIA
  • Domaine : Informatique/Ingénierie assistée par ordinateur
  • Mots-clés : Best approximation – Chebyshev polynomial – Uniform norm
 
  • inria-00201893, version 1
  • http://hal.inria.fr/inria-00201893
  • oai:hal.inria.fr:inria-00201893
  • Contributeur : Chine Publications Liama <>
  • Soumis le : Jeudi 3 Janvier 2008, 14:35:56
  • Dernière modification le : Jeudi 3 Janvier 2008, 14:35:56