ISSN:
1432-0940
Keywords:
41A20
;
41A25
;
41A44
;
Rational approximants
;
Best rational approximation
;
Poles
;
Zeros
;
Extreme points of best approximants
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The asymptotic distribution (forn→∞) of poles and zeros of best rational approximantsr n * ∈R nn of the function |x| on [−1, 1] as well as the asymptotic distribution of extreme points of the error function |x|−r n * (x) on [−1, 1] is investigated. The precision of the asymptotic formulae corresponds to that of the strong error formula $$\lim _{n \to \infty } e^{\pi \sqrt n } E_{nn} (|x|,[ - 1,1]) = 8$$ , which has been proved in [St1]. Here,E nn (|x|, [−1, 1]) denotes the minimal approximation error in the uniform norm on [−1, 1]. The accuracy of the asymptotic distribution functions is so high that the location of individual poles, zeros, and extreme points can be distinguished forn sufficiently large.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01303523
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