On the rate of convergence of iterated exponentials

Fuchang Gao; Lixing Han; Kenneth Schilling

doi:10.1007/s12190-011-0511-2

Journal of Applied Mathematics and Computing

June 2012, Volume 39, Issue 1, pp 89–96

On the rate of convergence of iterated exponentials

Authors

Fuchang Gao
- Department of MathematicsUniversity of Idaho
Lixing Han
Email author
- Department of MathematicsUniversity of Michigan-Flint
Kenneth Schilling
- Department of MathematicsUniversity of Michigan-Flint

Article

First Online:: 14 September 2011

Received:: 19 May 2011

DOI: 10.1007/s12190-011-0511-2

Cite this article as:: Gao, F., Han, L. & Schilling, K. J. Appl. Math. Comput. (2012) 39: 89. doi:10.1007/s12190-011-0511-2

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Abstract

We study the asymptotic rate of convergence of the sequence of iterated exponentials \(\{ z_{1}=a, z_{n+1}=a^{z_{n}}, n \geq 1 \}\). 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.

Keywords

Iterated exponentialsRate of convergence

Mathematics Subject Classification (2000)

41A2540A05

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On the rate of convergence of iterated exponentials

Authors

Abstract

Keywords

Mathematics Subject Classification (2000)

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