The mechanism of the multivariate Pade process

Abstract

In [3] (n,m) multivariate Padé approximants were introduced by means of a shift of the degrees in numerator and denominator over nm This definition is repeated here in section 3. In various papers many properties of those Padé approximants were proved; the analogy with the univariate case is remarkable. Here we show that the shift of the degrees over nm also arises in a natural way if we want to preserve some numerical algorithms or some geometrical pictures. Thus the paper provides new insights into the mechanism of the multivariate Padé process, and also some compact formulas for the multivariate Padé approximant itself.