On the Convergence of General Order Multivariate Padé-Type Approximants Original Research Article

In previous papers the convergence of sequences of “rectangular” multivariate Padé-type approximants was studied. In other publications definitions of “triangular” multivariate Padé-type approximants were given. We extend these results to the general order definition where the choice of the denominator polynomial is completely free. Also we develop convergence theorems and we distinguish between results obtained in polydiscs and in multivariate balls. The numerical examples section illustrates this difference and compares the obtained results with the approximation power of general order multivariate Padé approximants.