Multivariate Padé approximation

摘要

This paper is a survey on the multivariate Padé approximation. Two types of approximants are considered: those which can approximate general meromorphic functions f=h/g where both h and g are holomorphic, and those which are specialized to the approximation of functions of the same form where g is a polynomial. Algorithms are described, together with the different techniques used for proving convergence.