New bounds on the Lebesgue constants of Leja sequences on the unit disc\n and their projections Re-Leja sequences

2015/03/05 by Abdellah Chkifa, Chkifa, Abdellah
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1503.01731

openalex publication_date 2015/03/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In the papers [6, 7] we have established linear and quadratic bounds, in k,\non the growth of the Lebesgue constants associated with the k-sections of\nLeja sequences on the unit disc \U and Re-Leja sequences obtained\nfrom the latter by projection into [-1, 1]. In this paper, we improve these\nbounds and derive sub-linear and sub-quadratic bounds. The main novelty is the\nintroduction of a "quadratic" Lebesgue function for Leja sequences on\n\U which exploits perfectly the binary structure of such sequences\nand can be sharply bounded. This yields new bounds on the Lebesgue constants of\nsuch sequences, that are almost of order \√(k) when k has a sparse\nbinary expansion. It also yields an improvement on the Lebesgue constants\nassociated with Re-Leja sequences.\n

Related

• A sharp bound on the Lebesgue constant for Leja points in the unit disk
• A uniform bound for the Lagrange polynomials of Leja points for the unit disk and applications in multivariate Lagrange interpolation
• A simple upper bound for Lebesgue constants associated with Leja points on the real line
• On the Lebesgue Constant of Weighted Leja Points for Lagrange Interpolation on Unbounded Domains
• Multidimensional intertwining Leja sequences and applications in\n bidimensional Lagrange interpolation