A new approach to vector-valued rational interpolation
type: Item
instance of: scholarly article
title: A new approach to vector-valued rational interpolation
zbMATH Open document ID: 1065.41022
author: Avram Sidi
published in: Journal of Approximation Theory
publication date: 2005-02-22T00:00:00Z
review text: The author gave the general framework within which a whole family of vector-valued rational interpolants was defined. The author introduced three different types of criteria to obtain the three types of rational interpolation procedures and developed algorithms for constructing the resulting rational functionals. The author derived determinantal representation for these rational interpolants. These determinantal representations may serve as a useful tool in the (de Montessus type) convergence analysis of the interpolants as the degree of their numerators tends to infinity while the degree of their denominators is kept fixed. This approach was used successfully in the paper of \textit{A. Sidi} [''Rational approximations from power series of vector-valued mermorphic function'', J. Approx. Theory 77, No.1, 89--111 (1994; Zbl 0808.41010)].
reviewed by: Bhavana Deshpande
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 2137004
zbMATH Keywords: Vector-valued rational interpolation
zbMATH Keywords: Vector-valued rational approximation
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: Newton interpolation formula
zbMATH Keywords: Padé approximants
MaRDI profile type: Publication
full work available at URL: j.jat.2004.06.005
OpenAlex ID: W2053165063
cites work: Vector valued rational interpolants. I
cites work: Vector-valued Rational Interpolants II
cites work: Vector-valued, rational interpolants. III
cites work: Rational approximations from power series of vector-valued meromorphic functions
cites work: Application of Vector-Valued Rational Approximations to the Matrix Eigenvalue Problem and Connections with Krylov Subspace Methods
cites work: A new approach to the rational interpolation problem: The vector case
DOI: 10.1016/J.JAT.2004.06.005
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description: scientific article; zbMATH DE number 2137004