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Zbl 0791.41018
Kroó, András; Peherstorfer, Franz
On the asymptotic distribution of oscillation points in rational approximation. (English)
[J] Anal. Math. 19, No.3, 225-232 (1993). ISSN 0133-3852; ISSN 1588-273X/e

Let $R\sb{m,n}$ denote the set of algebraic rational functions of degree $(m,n)$ on $[-1,1]$. For $f\in C[-1,1]$ the distribution of the oscillation points of the best uniform rational approximation to $f$ from $R\sb{m,n}$ is studied. For $n=0$, $m\to\infty$, Kadec proved that one gets uniform distribution of the oscillatory points (with respect to Chebyshev measure). This result was shown recently by Borwein, Grothmann, Kroó and Saff to still hold if $n=n(m)$ with $n=o(m)$; whereas, for $n=m-1$, it was shown to no longer be true. In this paper, it is shown that Kadec's result also holds for $n=[cm]$ with $0<c<1$, which had remained open in the previous paper.
[G.D.Taylor (Fort Collins)]

MSC 2000:: *41A20 Approximation by rational functions
41A50 Best approximation

Keywords: best uniform rational approximation

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