Skip to Main content Skip to Navigation
Journal articles

Best uniform approximation to a class of rational functions

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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [9 references]  Display  Hide  Download

https://hal.inria.fr/inria-00517597
Contributor : Thss Tsinghua <>
Submitted on : Wednesday, September 15, 2010 - 3:30:05 AM
Last modification on : Tuesday, December 18, 2018 - 10:56:29 AM
Long-term archiving on: : Friday, December 2, 2016 - 5:04:41 AM

File

Zhitong_Zheng2007a.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Zhitong Zheng, Jun-Hai Yong. Best uniform approximation to a class of rational functions. Journal of Mathematical Analysis and Applications, Elsevier, 2007, 334 (2), pp.909-921. ⟨10.1016/j.jmaa.2006.10.047⟩. ⟨inria-00517597⟩

Share

Metrics

Record views

140

Files downloads

364