Construction of new generalizations of Wynn’s epsilon and rho algorithm by solving finite difference equations in the transformation order

Abstract

We construct new sequence transformations based on Wynn's epsilon and rho algorithms. The recursions of the new algorithms include the recursions of Wynn's epsilon and rho algorithm and of Osada's generalized rho algorithm as special cases. We demonstrate the performance of our algorithms numerically by applying them to some linearly and logarithmically convergent sequences as well as some divergent series.

Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations

“…Many of the infinite‐dimensional discrete integrable models that are supported by (in the sense that they can be reduced to) integrable symplectic maps have interesting properties: the existence of Lax pairs, Bäcklund transformations, symmetries and conservation laws, Hamiltonian structures, the construction of integrable algorithms, (elliptic) soliton solutions, finite genus solutions [see Refs. 10–23, and references therein].…”