Multivariate Frobenius–Padé approximants: Properties and algorithms

Frobenius-Padé approximants for d-orthogonal series: theory and computational aspects

This work is about Frobenius-Padé approximants for series of orthogonal polynomials of dimension d (d ∈ N). Concerning to the series, we give the projection property of partial sums, we show how to compute their coe cients, and how to get the coe cients of the product of a series by a polynomial. Concerning to the approximants we work essentially about their recursive computation. Also, we give...

Generic properties of Padé approximants and Padé universal series

We establish properties concerning the distribution of poles of Padé approximants, which are generic in Baire category sense. We also investigate Padé universal series, an analog of classical universal series, where Taylor partial sums are replaced with Padé approximants. In particular, we complement previous studies on this subject by exhibiting dense or closed infinite dimensional linear subs...

Szegő-type Asymptotics for Ray Sequences of Frobenius-padé Approximants

Let σ̂ be a Cauchy transform of a possibly complex-valued Borel measure σ and {pn} be a system of orthonormal polynomials with respect to a measure μ, supp(μ)∩ supp(σ) = ∅. An (m,n)-th Frobenius-Padé approximant to σ̂ is a rational function P/Q, deg(P) 6m, deg(Q) 6 n, such that the first m+n+ 1 Fourier coefficients of the linear form Qσ̂−P vanish when the form is developed into a series with respe...

On the convergence of multivariate Padé approximants

While the concept of Padé approximant is essentially several centuries old, its multivariate version dates only from the early seventies. In the last century many univariate convergence results were proven, describing the approximation power for several function classes. It is not our aim to give a general review of the univariate case, but to discuss only these theorems that have a multivariat...

On nonstandard Padé approximants suitable for effective properties of two-phase composite materials