GENERALIZED MULTIVARIATE PADE APPROXIMANTS

A new definition of multivariate Pade approximation is introduced, whi ch is a natural generalization of the univariate Pade approximation an d consists in replacing the exact interpolation problem by a least squ ares interpolation. This new definition allows a straightforward exten sion of the Montessus de Ballore theorem to the multivariate case. Exc ept for the particular case of the so-called homogeneous Pade approxim ants, this extension has up to now been impossible to obtain in the cl assical formulation of the multivariate Padi approximation. Besides, t he least squares formulation can also be applied to the univariate cas e, and provides an alternative to the classical Pade interpolation. (C ) 1998 Academic Press.