Existence of certain sequences of Hermite-Padé approximants
type: Item
instance of: scholarly article
title: Existence of certain sequences of Hermite-Padé approximants
zbMATH Open document ID: 0817.41021
DOI: 10.1016/0377-0427(94)90393-X
published in: Journal of Computational and Applied Mathematics
publication date: 1995-04-02T00:00:00Z
review text: Hermite-Padé polynomials are defined by equating the coefficients of powers of \(z\) in the equation \[ \sum^ k_{j=- 1} f_ j(z) Q_ j(z)= O(z^{s+ 1}), \] where the \(f_ j(z)\) are formal power series in \(z\), the \(Q_ j(z)\) are polynomials of degree \(m_ j\) and \(s= \sum^ k_{j= -1} (m_ j+ 1)- 2\). In the paper a notion of minimality is introduced, and then it is shown that there exists an infinite sequence of unique, minimal Hermite-Padé polynomials of horizontal, near-partially-diagonal and near-diagonal character.
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 739570
zbMATH Keywords: Hermite-Padé polynomials
author: George A. jun. Baker
author: Peter R. Graves-Morris
reviewed by: Herbert Stahl
MaRDI profile type: Publication
cites work: Definition and uniqueness of integral approximants
cites work: Determinants and the structure of the integral approximant table
cites work: The structure of the singular solution table of the M-Padé approximation problem
cites work: Hermite-Padé approximation (basic notions and theorems)
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description: scientific article; zbMATH DE number 739570