On the asymptotic distribution of oscillation points in rational approximation
type: Item
instance of: scholarly article
title: On the asymptotic distribution of oscillation points in rational approximation
zbMATH Open document ID: 0791.41018
DOI: 10.1007/BF02074000
author: András Kroó
author: Franz Peherstorfer
published in: Analysis Mathematica
publication date: 1994-03-22T00:00:00Z
review text: Let \(R_{m,n}\) 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 \(R_{m,n}\) 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.
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 536535
zbMATH Keywords: best uniform rational approximation
MaRDI profile type: Publication
cites work: Approximations with negative roots and poles
cites work: The Density of Alternation Points in Rational Approximation
cites work: Interpolatory properties of best rational \(L_ 1\)-approximations
cites work: The Density of Extreme Points in Complex Polynomial Approximation
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cites work: On the rational Tschebyscheff operator
full work available at URL: https://doi.org/10.1007/bf02074000
OpenAlex ID: W60518112
description: scientific article; zbMATH DE number 536535