Newton-Thiele's rational interpolants
type: Item
instance of: scholarly article
title: Newton-Thiele's rational interpolants
zbMATH Open document ID: 0965.41007
DOI: 10.1023/A:1019193210259
author: Yi Fang
author: Jieqing Tan
published in: Numerical Algorithms
publication date: 2000-11-22T00:00:00Z
review text: For the interpolation of a bivariate function \(f(x,y)\), one can construct a Newton interpolating polynomial in \(x\) whose coefficients are Newton interpolating polynomials in \(y\). This is the bivariate Newton interpolating polynomial. To construct a rational interpolant one can construct a Thiele continued fraction in \(x\) whose coefficients are Thiele continued fractions in \(y\). This is a branched continued fraction interpolant. Thiele-Newton rational interpolants use a Thiele continued fraction in \(x\) with coefficients that are Newton polynomials in \(y\). Newton-Thiele interpolants are like Thiele-Newton interpolants with the role of Thiele continued fraction and Newton polynomial interchanged. The latter are the subject of this paper. They are constructed using ``blending differences'' which is a new type of differences being a mixture of divided differences and inverse differences. This paper gives a constructive algorithm to compute these interpolants, discusses an expression for the interpolation error and considers the confluent case when the grid of interpolations collapses to one point.
reviewed by: Adhemar Bultheel
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 65D05
zbMATH DE Number: 1534768
zbMATH Keywords: continued fractions
zbMATH Keywords: rational interpolation
zbMATH Keywords: Thiele fraction
zbMATH Keywords: Newton interpolation
MaRDI profile type: Publication
full work available at URL: a:1019193210259
OpenAlex ID: W102329879
description: scientific article; zbMATH DE number 1534768