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What is Best Uniform Approximation to a Class of Rational Functions about?

We explicitly determine the best uniform polynomial approximation p \* n-1 to a class of rational functions of the form 1/(xc) 2 + K(a, b, c, n)/(xc) 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.

Author

Zhitong Zheng; Jun-Hai Yong

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2007

Language

EN