On the rate of convergence of iterated exponentials

被引：1
作者：
Fuchang Gao
Lixing Han
Kenneth Schilling
机构：
[1] Department of Mathematics, University of Idaho, Moscow
[2] Department of Mathematics, University of Michigan-Flint, Flint
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：
学科分类号：
摘要：
We study the asymptotic rate of convergence of the sequence of iterated exponentials {z1=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. © 2011 Korean Society for Computational and Applied Mathematics.
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页码：89 / 96
页数：7
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