Multivariate approximants with Levin-like transforms

It is well known that Levin-like univariate approximants work better than Padé approximants for a large class of functions. We propose to investigate the Levin-like multivariate approximants. It is shown that a simple modification of the qd-algorithm makes it possible to construct the homogeneous multivariate Padé approximants of order [n,n] and [n,n+1]. We demonstrate how to construct the homogeneous and nested Levin-like approximants and compare their effectiveness with the homogeneous and nested Padé approximants which exhaust the same number of terms of a series in more than one variable. It is found that the Levin-like multivariate approximants are much more effective for a large class of functions.