On the rate of convergence of iterated exponentials

被引：0
|
作者：
Gao, Fuchang [1 ]
Han, Lixing [2 ]
Schilling, Kenneth [2 ]
机构：
[1] Univ Idaho, Dept Math, Moscow, ID 83844 USA
[2] Univ Michigan Flint, Dept Math, Flint, MI 48502 USA
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2012年 / 39卷 / 1-2期
关键词：
Iterated exponentials; Rate of convergence;
D O I：
10.1007/s12190-011-0511-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the asymptotic rate of convergence of the sequence of iterated exponentials {z(1) = a, z(n+1) = a(zn), n >= 1}. We show that z(n) converges at a linear rate if a is in the interior of the Baker-Rippon convergence region and at a sublinear rate if a is on its boundary. A precise characterization of the rate is explored when the sequence converges sublinearly.
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页码：89 / 96
页数：8
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