Frobenius-Padé approximants for d-orthogonal series: theory and computational aspects
نویسندگان
چکیده
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 several examples and numerical results.
منابع مشابه
Multivariate Frobenius–Padé approximants: Properties and algorithms
The aim of this paper is to construct rational approximants for multivariate functions given by their expansion in an orthogonal polynomial system. This will be done by generalizing the concept of multivariate Padé approximation.After defining themultivariate Frobenius–Padé approximants, we will be interested in the two following problems: the first one is to develop recursive algorithms for th...
متن کاملSzegő-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...
متن کاملImprovement of the method of diagonal Padé approximants for perturbative series in gauge theories
Recently it has been pointed out that diagonal Padé approximants to truncated perturbative series in gauge theories have the remarkable property of being independent of the choice of the renormalization scale as long as the gauge coupling parameter α(p2) is taken to evolve according to the one-loop renormalization group equation – i.e., in the large-β0 approximation. In this letter we propose a...
متن کاملGeneric 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...
متن کاملPadé approximants and the prediction of non-perturbative parameters in particle physics
Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Padé approximants to meromorphic functions. However, only recently this connection has been acknowledged and efforts at fully exploiting it are only starting. In this article I will briefly review the most prominent techniques used in no...
متن کامل