- Tytuł:
- Asymptotic distribution of poles and zeros of best rational approximants to $x^α$ on [0,1]
- Autorzy:
-
Saff, E.
Stahl, H. - Powiązania:
- https://bibliotekanauki.pl/articles/1360089.pdf
- Data publikacji:
- 1995
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
rational approximation
best approximation
distribution of poles and zeros - Opis:
- 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.
- Źródło:
-
Banach Center Publications; 1995, 31, 1; 329-348
0137-6934 - Pojawia się w:
- Banach Center Publications
- Dostawca treści:
- Biblioteka Nauki
Artykuł