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Zbl 1072.41005
Blatt, Hans-Peter
The interaction of alternation points and poles in rational approximation. (English)
[J] J. Comput. Appl. Math. 179, No. 1-2, 31-46 (2005). ISSN 0377-0427

The author investigates the interrelation of alternation points for the minimal error function and poles of best Chebyshev approximants if uniform approximation on the interval $[-1, 1]$ by rational functions of degree $(n(s), m(s))$ is considered, $s \in N$. He shows that at least for a subsequence $\Lambda \subset N$, the asymptotic behaviour of the alternation points of the degree $(n(s), m(s))$, $s \in\Lambda$ is completely determined by the location of the poles of the best approximants and vice versa, if $m(s) \leq n(s)$ or $m(s) - n(s) = o(s/\log s)$ as $s \to\infty$.
[Bhavana Deshpande (Ratlam)]

MSC 2000:: *41A20 Approximation by rational functions

Keywords: Rational approximation

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