# Asymptotic distribution of poles and zeros of best rational approximants to ${x}^{\alpha}$ on [0,1]

Banach Center Publications (1995)

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

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topSaff, 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 -

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