On the Lebesgue constant of the trigonometric Floater-Hormann rational interpolant at equally spaced nodes
| Title | On the Lebesgue constant of the trigonometric Floater-Hormann rational interpolant at equally spaced nodes |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Bandiziol, C, De Marchi, S |
| Journal | Dolomites Research Notes on Approximation |
| Volume | 12 |
| Issue | 1 |
| Pagination | 51-67 |
| Date Published | 06/2019 |
| Publisher | Padova University Press |
| Place Published | Padova, IT |
| ISSN Number | 2035-6803 |
| Keywords | barycentric rational interpolation, Lebesgue constant, trigonometric interpolation |
| 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 |
| URL | https://drna.padovauniversitypress.it/2019/1/6 |
| DOI | 10.14658/pupj-drna-2019-1-6 |
