作者：
Brezinski, ClaudeHe, YiHu, Xing-BiaoRedivo-Zaglia, MichelaSun, Jian-QingLaboratoire Paul Painlevé
UMR CNRS 8524 UFR de Mathématiques Pures et Appliquées Université des Sciences et Technologies de Lille France LSEC
Institute of Computational Mathematics and Scientific Engineering Computing AMSS Chinese Academy of Sciences and Graduate School of the Chinese Academy of Sciences Beijing People’s Republic of China LSEC
Institute of Computational Mathematics and Scientific Engineering Computing AMSS Chinese Academy of Sciences Beijing People’s Republic of China Università degli Studi di Padova
Dipartimento di Matematica Pura ed Applicata Italy
Abstract: In this paper, we propose a multistep extension of the Shanks sequence transformation. It is defined as a ratio of determinants. Then, we show that this transformation can be recursively implemented ...
详细信息
Abstract: In this paper, we propose a multistep extension of the Shanks sequence transformation. It is defined as a ratio of determinants. Then, we show that this transformation can be recursively implemented by a multistep extension of the $\varepsilon$–algorithm of Wynn. Some of their properties are specified. Thereafter, the multistep $\varepsilon$–algorithm and the multistep Shanks transformation are proved to be related to an extended discrete Lotka–Volterra system. These results are obtained by using Hirota’s bilinear method, a procedure quite useful in the solution of nonlinear partial differential and difference equations.
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