Discrete soliton equations and convergence acceleration algorithms
Atsushi Nagai, Junkichi Satsuma
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 η-algorithm is nothing but the discrete KdV equation. In addition, one generalized version of the ρ-algorithm is considered to be integrable discretization of the cylindrical KdV equation.
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