Multivariate reciprocal differences for branched Thiele continued fraction expansions
type: Item
instance of: scholarly article
title: Multivariate reciprocal differences for branched Thiele continued fraction expansions
zbMATH Open document ID: 0638.65014
DOI: 10.1016/0377-0427(88)90264-6
author: Annie Cuyt
author: Brigitte M. Verdonk
published in: Journal of Computational and Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: For a multivariate function a Viscovatov-like algorithm for the construction of a branched continued fraction expansion was developed independently by \textit{J. A Murphy} and \textit{M. R. O'Donohoe} [ibid. 4, 181-190 (1978; Zbl 0407.40002)] and by \textit{K. J. Kuchminskaya} [Dopov. Akad. Nauk Ukr. RSR, Ser. A 1978, 613-617 (1978; Zbl 0418.40003)]. On the other hand, multivariate inverse difference to construct Thiele interpolating branched continued fractions were introduced independently by \textit{Kh. J. Kuchminskaya} [Mat. Metody Fiz.-Mekh. Polya 12, 3-10 (1980; Zbl 0439.41006)] and by the author of this paper [Computing 34, 41-61 (1985; Zbl 0553.41004)]. The purpose of this paper is to show the link between these two approaches in the multivariate case by introducing different multivariate reciprocal differences so as to obtain the branched continued fraction expansion as the limiting value of the Thiele interpolating branched continued fraction.
Mathematics Subject Classification ID: 65D15
Mathematics Subject Classification ID: 65B05
Mathematics Subject Classification ID: 40A15
zbMATH DE Number: 4041144
zbMATH Keywords: multivariate function
zbMATH Keywords: Viscovatov-like algorithm
zbMATH Keywords: branched continued fraction expansion
zbMATH Keywords: multivariate inverse difference
zbMATH Keywords: Thiele interpolating branched continued fractions
zbMATH Keywords: multivariate reciprocal differences
reviewed by: R. S. Dahiya
MaRDI profile type: Publication
full work available at URL: 0377-0427(88)90264-6
OpenAlex ID: W1973586116
cites work: A review of multivariate Padé approximation theory
cites work: A review of branched continued fraction theory for the construction of multivariate rational approximants
cites work: Multivariate rational interpolation
cites work: Q3881271
cites work: Q3721099
cites work: Q3762768
cites work: Q3780406
cites work: A two-variable generalization of the Stieltjes-type continued fraction
cites work: Automatic differentiation: techniques and applications
cites work: Thiele-type branched continued fractions for two-variable functions
description: scientific article; zbMATH DE number 4041144