Generalized Multivariate Padé Approximants Original Research Article

A new definition of multivariate Padé approximation is introduced, which is a natural generalization of the univariate Padé approximation and consists in replacing the exact interpolation problem by a least squares interpolation. This new definition allows a straightforward extension of the Montessus de Ballore theorem to the multivariate case. Except for the particular case of the so-called homogeneous Padé approximants, this extension has up to now been impossible to obtain in the classical formulation of the multivariate Padé approximation. Besides, the least squares formulation can also be applied to the univariate case, and provides an alternative to the classical Padé interpolation.