On the Lebesgue constant of the trigonometric Floater-Hormann rational interpolant at equally spaced nodes

Abstract

It is well known that the classical polynomial interpolation gives bad approximation if the nodes are equispaced. A valid alternative is the family of barycentric rational interpolants introduced by Berrut in [4], analyzed in terms of stability by Berrut and Mittelmann in [5] and their extension done by Floater and Hormann in [8]. In this paper firstly we extend them to the trigonometric case, then as in the Floater-Hormann classical interpolant, we study the growth of the Lebesgue constant on equally spaced points. We show that the growth is logarithmic providing a stable interpolation operator

De Marchi S., Bandiziol C. (2019) "On the Lebesgue constant of the trigonometric Floater-Hormann rational interpolant at equally spaced nodes " Dolomites Research Notes on Approximation, 12(1), 51-67. DOI: 10.14658/PUPJ-DRNA-2019-1-6  
Year of Publication
2019
Journal
Dolomites Research Notes on Approximation
Volume
12
Issue Number
1
Start Page
51
Last Page
67
Date Published
06/2019
ISSN Number
2035-6803
Serial Article Number
6
DOI
10.14658/PUPJ-DRNA-2019-1-6
Issue
Section
Articles