An Extension of the Steffensen Iteration and Its Computational Complexity
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概要
- 論文の詳細を見る
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.
- 東北大学の論文
著者
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Kondo Koichi
Department Of Applied Fine Chemistry Faculty Of Engineering Osaka University
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Nakamura Yoshimasa
Department Of Applied Mathematics And Physics Faculty Of Engineering Kyoto University
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Nakamura Yoshimasa
Department Of Informatics And Mathematical Science Graduate School Of Engineering Science Osaka Univ
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Kondo Koichi
Department Of Informatics And Mathematical Science Graduate School Of Engineering Science Osaka Univ
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