On rational interpolation to meromophic functions in several variables
A well-known method for constructing rational approximants in one complex variable is Padé-type approximation, where in contrast to the classical Padé approximation the denominator polynomials are restricted in some sense. In this paper, a new Padé-type approach to rational approximation in several variables is presented. The denominators are chosen in such a way that an analogue to the well-known Montessus de Ballore theorem is valid under certain conditions. Moreover, it turns out that in the univariate case, the corresponding approximants coincide with the Padé approximants. Several examples throw some light on the sharpness of the convergence results.
scientific article; zbMATH DE number 1523562
scientific article