A fast, reliable algorithm for calculating Pade′-Hermite forms

摘要

We present a new fast algorithm for the calculation of a Pade-Hermite form for a vector of power series. When the vector of power series is normal, the algorithm is shown to calculate a Pade-Hermite form of type (n0, ··· , nk) in O(k·(n02 + ··· + nk2)) operations. This complexity is the same as that of other fast algorithms for computing Pade-Hermite approximants. However, unlike other algorithms, the new algorithm also succeeds in the non-normal case, usually with only a moderate increase in cost.