A comparison of algorithms for the symbolic computation of Padé approximants
This paper compares three algorithms for the symbolic computation of Padé approximants: an 0(n3) algorithm based on the direct solution of the Hankel linear system exploiting only the property of symmetry, an 0(n2) algorithm based on the extended Euclidean algorithm, and an 0(n log2n) algorithm based on a divide-and-conquer version of the extended Euclidean algorithm. Implementations of these algorithms are presented and some timing comparisons are given. It is found that the 0(n2) algorithm is often the fastest for practical sizes of problems and, surprisingly, the 0(n3) algorithm wins in the important case where the power series being approximated has an exact rational function representation.
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