Fraction-free computation of simultaneous padé approximants
Bernhard Beckermann, George Labahn · 2009
In this paper we give a new, fast algorithm for solving the simultaneous Padé approximation problem. The algorithm is fraction-free and is suitable for computation in domains where growth of coefficients in intermediate computations are a central concern. The algorithm gives significant improvement on previous fraction-free methods, in particular when solved via the use of vector Hermite-Padé approximation using the FFFG order basis algorithm previously done by the authors. The improvements are both in terms of bit complexity and in reduced size of the intermediate quantities.