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

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Saff E. B., Stahl H.

Banach Center Publications

1995

tom 31

nr 1

329-348

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.

Ograniczanie wyników

1 Banach Center Publications

1 Saff E. B.

1 Stahl H.

1 1995

Wyniki wyszukiwania

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