On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains. (23rd June 2018)

• Record Type: Journal Article
• Authors: Jantsch, Peter; Webster, Clayton G; Zhang, Guannan
• Is Part Of: IMA journal of numerical analysis. Volume 39:Number 2(2019)
• Page Start: 1039
• Page End: 1057
• Publication Date: 2018-06-23
• Subjects: weighted Leja sequence -- Lagrange interpolation -- Lebesgue constant; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry002
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: This work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function$w:\mathbb{R}\rightarrow [0, 1]$ . Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.