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

Saff, E.; Stahl, H.

Asymptotic distribution of poles and zeros of best rational approximants to

x^{α}

on [0,1]

Saff, E. ; Stahl, H.

Banach Center Publications, Tome 31 (1995), p. 329-348 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let $r_{n} * \in ℛ_{n n}$ 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 $ℝ_{< 0}$ . 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.

Publié le : 1995-01-01

Zbl 0826.41018

EUDML-ID : urn:eudml:doc:262780

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     title = {Asymptotic distribution of poles and zeros of best rational approximants to $x^$\alpha$$ on [0,1]},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {329-348},
     zbl = {0826.41018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p329bwm}
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Saff, E.; Stahl, H. Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1]. Banach Center Publications, Tome 31 (1995) pp. 329-348. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p329bwm/

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