Abstract
The M-Padé approximation problem is defined which contains as a special case the Hermite-Padé approximation as well as the Newton-Padé approximation. Different well-known methods for computing M-Padé approximations are studied, they are based on a normal solution table. It is shown that the concept of one of them — computing bases of sets induced by interpolation conditions — can be generalized to the singular case. A characterization of special bases leads to a representation of the M-Padé solution set like in Beckermann (this journal, 1990); a simple, efficient and reliable method for computing such bases by so-called transfer matrices is derived. Finally, examples of Hermite-Padé and Newton-Padé approximation are given. The connection to other well-known reliable algorithms for rational interpolation is discussed.
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