Discrete soliton equations and convergence acceleration algorithms

Abstract

Some of the well-known convergence acceleration algorithms, when viewed as two-variable difference equations, are equivalent to discrete soliton equations. It is shown that the $\eta -$algorithm is nothing but the discrete KdV equation. In addition, one generalized version of the $\rho -$algorithm is considered to be integrable discretization of the cylindrical KdV equation.

11 pages, LaTeX file, no figures

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