inria-00201893, version 1
Best uniform approximation to a class of rational functions
Journal of Mathematical Analysis and applications 334 (2007) 909-921
Abstract: 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:
- Tsinghua University
- 2:
- 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
- Domain : Computer Science/Computer Aided Engineering
- Keywords : Best approximation – Chebyshev polynomial – Uniform norm
- inria-00201893, version 1
- http://hal.inria.fr/inria-00201893
- oai:hal.inria.fr:inria-00201893
- From:
- Submitted on: Thursday, 3 January 2008 14:35:56
- Updated on: Thursday, 3 January 2008 14:35:56
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