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The Toda molecule equation and the $\varepsilon$-algorithm


Authors: Atsushi Nagai, Tetsuji Tokihiro and Junkichi Satsuma
Journal: Math. Comp. 67 (1998), 1565-1575
MSC (1991): Primary 58F07, 65B10
DOI: https://doi.org/10.1090/S0025-5718-98-00987-9
MathSciNet review: 1484902
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Abstract: One of the well-known convergence acceleration methods, the $\varepsilon$-algorithm is investigated from the viewpoint of the Toda molecule equation. It is shown that the error caused by the algorithm is evaluated by means of solutions for the equation. The acceleration algorithm based on the discrete Toda molecule equation is also presented.


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Additional Information

Atsushi Nagai
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153, Japan
Email: slime@poisson.ms.u-tokyo.ac.jp

Tetsuji Tokihiro
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153, Japan
Email: toki@sunflower.t.u-tokyo.ac.jp

Junkichi Satsuma
Affiliation: Department of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153, Japan
Email: satsuma@poisson.ms.u-tokyo.ac.jp

DOI: https://doi.org/10.1090/S0025-5718-98-00987-9
Keywords: Toda molecule equation, $\varepsilon$-algorithm, Pad\'{e} approximation, continued fraction
Received by editor(s): May 20, 1996
Received by editor(s) in revised form: November 5, 1996, and February 13, 1997
Article copyright: © Copyright 1998 American Mathematical Society