Asymptotic distribution of poles and zeros of best rational approximants to x α on [0,1]

E. Saff; H. Stahl

Banach Center Publications (1995)

  • Volume: 31, Issue: 1, page 329-348
  • ISSN: 0137-6934

Abstract

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Let r n * n n be the best rational approximant to f ( x ) = x α , 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of r n * lie on the negative axis < 0 . In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function e n = f - r n * on [0,1], and survey related convergence results.

How to cite

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Saff, E., and Stahl, H.. "Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1]." Banach Center Publications 31.1 (1995): 329-348. <http://eudml.org/doc/262780>.

@article{Saff1995,
abstract = {Let $r_n* ∈ ℛ_\{nn\}$ be the best rational approximant to $f(x) = x^α$, 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of $r_n*$ lie on the negative axis $ℝ_\{<0\}$. In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function $e_n = f - r_n*$ on [0,1], and survey related convergence results.},
author = {Saff, E., Stahl, H.},
journal = {Banach Center Publications},
keywords = {rational approximation; best approximation; distribution of poles and zeros},
language = {eng},
number = {1},
pages = {329-348},
title = {Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1]},
url = {http://eudml.org/doc/262780},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Saff, E.
AU - Stahl, H.
TI - Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1]
JO - Banach Center Publications
PY - 1995
VL - 31
IS - 1
SP - 329
EP - 348
AB - Let $r_n* ∈ ℛ_{nn}$ be the best rational approximant to $f(x) = x^α$, 1 > α > 0, on [0,1] in the uniform norm. It is well known that all poles and zeros of $r_n*$ lie on the negative axis $ℝ_{<0}$. In the present paper we investigate the asymptotic distribution of these poles and zeros as n → ∞. In addition we determine the asymptotic distribution of the extreme points of the error function $e_n = f - r_n*$ on [0,1], and survey related convergence results.
LA - eng
KW - rational approximation; best approximation; distribution of poles and zeros
UR - http://eudml.org/doc/262780
ER -

References

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