A Fast, Reliable Algorithm for Calculating Pad&-Hermite Forms

We present a new fast algorithm for the calculation of a Pad&Hermite form for a vector of power series. When the vector of power series is normal, the algorithm is shown to calculate a Pad&Hermite form of type (no,.., nk) in O(k+ $ +... + nl)) operations. This com-plexity is the same as that of other fast algo-rithms for computing Pad&Hermite approxi-mants. However, unlike other algorithms, the new algorithm also succeeds in the non-normal case, usually with only a moderate increase in cost. 1