A q-difference version of the ϵ-algorithm

Abstract

In this paper, a q-difference version of the -algorithm is proposed. By using determinant identities the solutions of an initial value problem thus arisen can be expressed as ratios of Hankel determinants. It is shown that in numerical analysis this algorithm can be used to compute the approximation limt→∞f(t), and in the field of integrable systems it could be viewed as the q-difference version of the modified Toda molecule equation.