Multistep epsilon-algorithm, Shanks' transformation, and Lotka-Volterra system by Hirota's method
Numerical Analysis
2010-12-30 v1
Abstract
In this paper, we give a multistep extension of the epsilon-algorithm of Wynn, and we show that it implements a multistep extension of the Shanks' sequence transformation which is defined by ratios of determinants. Reciprocally, the quantities defined in this transformation can be recursively computed by the multistep epsilon-algorithm. The multistep epsilon-algorithm and the multistep Shanks' transformation are related to an extended discrete Lotka-Volterra system. These results are obtained by using the Hirota's bilinear method, a procedure quite useful in the solution of nonlinear partial differential and difference equations.
Cite
@article{arxiv.1012.5744,
title = {Multistep epsilon-algorithm, Shanks' transformation, and Lotka-Volterra system by Hirota's method},
author = {Claude Brezinski and Yi He and Xing-Biao Hu and Michela Redivo-Zaglia and Jian-Qing Sun},
journal= {arXiv preprint arXiv:1012.5744},
year = {2010}
}