A review of multivariate Padé approximation theory

A review of multivariate Pad6 approximation theory

In the past decade a lot of work has been done on the subject of multivariate Pad6 approximation theory and so it would be interesting to compare some different definitions. Let us first take a look at the univariate case. It is well known that univariate Pad6 approximants can be obtained in several equivalent ways and that they satisfy some typical properties. We will briefly repeat the defini...

On the Froissart phenomenon in multivariate homogeneous Padé approximation

In univariate Padé approximation we learn from the Froissart phenomenon that Padé approximants to perturbed Taylor series expansions of rational functions exhibit almost cancelling polezero combinations that are unwanted. The location of these pole-zero pairs is given by the socalled Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in...

On Padé Approximation of Some Practical Functions

Multivariate Approximation: Theory and Applications

A set of irregularly distributed points is fitted to a Least-Squares approximating surface constructed as linear combination of wavelets. The construction proceeds adaptively on a coarse-to-fine refinement. We discuss by numerical experiments the efficiency of the method in relation to iterative solution procedures. Furthermore, we present extensions of the method that allow to cope with wrong ...

"Multivariate Approximation: Theory and Applications"

This introductory paper describes the main topics of this special issue, dedicated to Leonardo Traversoni, known at international level as the promoter of the conference series “Multivariate Approximation: Theory and Applications”, to celebrate his 60th birthday.