Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
An Extension of the Steffensen Iteration and Its Computational Complexity
Koichi KONDOYoshimasa NAKAMURA
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1998 Volume 4 Issue 2 Pages 129-138

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Abstract

An extension of the Steffensen iteration method for solving a single nonlinear equation is considered. The point is that the iteration function is defined by using the k -th Shanks transform. The convergence rate is shown to be of order k +1. The use of ε -algorithm avoids the direct calculation of Hankel determinants, which appear in the Shanks transform, and then diminishes the computational complexity. For a special case of the Kepler equation, it is shown that the numbers of mappings are actually decreased by the use of the extended Steffensen iteration.

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© 1998 by the Graduate School of Information Sciences (GSIS), Tohoku University
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