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This article is cited in 17 scientific papers (total in 17 papers)
Numerical results on best uniform rational approximation of $|x|$ on $[-1,1]$
R. S. Vargaa, A. Ruttana, A. J. Carpenterb a Kent State University
b Butler University
Abstract:
With $E_{n,n}(|x|;[-1,1])$ denoting the error of best uniform rational approximation from
$\pi_{n,n}$ to $|x|$ on $[-1,1]$, we determine the numbers
$\{E_{2n,2n}(|x|;[-1,1])\}_{n=1}^{40}$, where each of these numbers was calculated with a precision of at least 200 significant digits. With these numbers, the Richardson extrapolation method was applied to the products
$\{e^{\pi\sqrt{2n}}E_{2n,2n}(|x|;[-1,1])\}_{n=1}^{40}$, and it appears, to at least 10 significant digits, that
$$
8\stackrel{?}{=}\lim_{n\to\infty}e^{\pi\sqrt{2n}}E_{2n,2n}(|x|;[-1,1]),
$$
which gives rise to an interesting new conjecture in the theory of rational approximation.
Received: 12.10.1990
Citation:
R. S. Varga, A. Ruttan, A. J. Carpenter, “Numerical results on best uniform rational approximation of $|x|$ on $[-1,1]$”, Math. USSR-Sb., 74:2 (1993), 271–290
Linking options:
https://www.mathnet.ru/eng/sm1386https://doi.org/10.1070/SM1993v074n02ABEH003347 https://www.mathnet.ru/eng/sm/v182/i11/p1523
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Abstract page: | 477 | Russian version PDF: | 136 | English version PDF: | 23 | References: | 64 | First page: | 1 |
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