Exponentially convergent linear rational interpolation between equidistant (and other) points
type: Item
instance of: scholarly article
title: Exponentially convergent linear rational interpolation between equidistant (and other) points
zbMATH Open document ID: 0885.65008
author: Jean-Paul Berrut
author: Hans D. Mittelmann
published in: Methods and Applications of Analysis
publication date: 1998-04-20T00:00:00Z
review text: A linear rational method to interpolate continuous functions on an interval \([a,b]\), is considered. The usual way of obtaining linear rational approximants is by fixing the denominator -- of degree \(n\) -- whose zeros must only depend on the selected interpolation points, and considering all the numerators with degree not greater than \(N\). The main purpose of the article is to demonstrate how the convergence of these interpolants -- with slowly increasing Lebesgue constants -- can be improved by decreasing \(n\) from \(N\), keeping the Lebesgue constant small. Two sections are devoted to the numerical solution of the corresponding computational problems.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 1067297
zbMATH Keywords: linear rational interpolation
zbMATH Keywords: linear rational method
zbMATH Keywords: continuous functions
zbMATH Keywords: convergence
zbMATH Keywords: Lebesgue constants
reviewed by: J. Illán
MaRDI profile type: Publication
full work available at URL: maa.1997.v4.n1.a5
OpenAlex ID: W1523065035
DOI: 10.4310/MAA.1997.V4.N1.A5
description: scientific article; zbMATH DE number 1067297