On rational interpolation to meromorphic functions in several variables

In this paper, a new approach to construct rational interpolants to functions of several variables is considered. These new families of interpolants, which in fact an: particular cases of the so-called Pade-type approximants (that is, rational interpolants with prescribed denominators), extend the classical Fade approximants (for the univariate case) and provide rather general extensions of the well-known Montessus de Ballore theorem for several variables. The accuracy of these approximants and the sharpness of our convergence results are analyzed by means of several examples. (C) 2000 Academic Press.