Real vs. complex rational Chebyshev approximation on an interval

Authors:
Lloyd N. Trefethen and Martin H. Gutknecht

Journal:
Trans. Amer. Math. Soc. **280** (1983), 555-561

MSC:
Primary 41A25; Secondary 41A50

DOI:
https://doi.org/10.1090/S0002-9947-1983-0716837-X

MathSciNet review:
716837

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Abstract: If is real-valued, let and be the errors in best approximation to in the supremum norm by rational functions of type with real and complex coefficients, respectively. It has recently been observed that can occur for any , but for no is it known whether is zero or strictly positive. Here we show that both are possible: , but for . Related results are obtained for approximation on regions in the plane.

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DOI:
https://doi.org/10.1090/S0002-9947-1983-0716837-X

Keywords:
Chebyshev approximation,
rational approximation

Article copyright:
© Copyright 1983
American Mathematical Society