A uniform bound for the Lagrange polynomials of Leja points for the unit disk and applications in multivariate Lagrange interpolation – I2M – Institut de Mathématique de Marseille

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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

A uniform bound for the Lagrange polynomials of Leja points for the unit disk and applications in multivariate Lagrange interpolation

Amadeo Irigoyen
University of Barcelona
https://www.researchgate.net/profile/Amadeo-Irigoyen

Date(s) : 02/10/2017 iCal
10h30 - 11h30

We study uniform estimates for the family of fundamental Lagrange polynomials associated with any Leja sequence for the complex unit disk.The main result claims that all these polynomials are uniformly bounded on the disk, i.e. independently of the range N of the associated N-Leja section. As a first application, we get an analogous estimate for any compact subset whose boundary is an Alper-smooth Jordan curve. We then deal with some applications in multivariate Lagrange interpolation. We first give some estimates of the Lebesgue constant for the intertwining sequence of Leja sequences. This result also requires an explicit formula for the associated fundamental Lagrange polynomials with uniform estimates. We finish by dealing with a method to get explicit bidimensional Leja sequences and then give a positive example for the bidisk.

https://arxiv.org/abs/1411.5527

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Analyse et Géométrie