On the Lebesgue Constant of Weighted Leja Points for Lagrange Interpolation on Unbounded Domains
Provides theoretical justification for using Leja points in interpolation on unbounded domains, which is foundational for high-dimensional approximation methods.
This paper analyzes the Lebesgue constant for weighted Leja points in Lagrange interpolation on unbounded domains, proving that it grows subexponentially with the number of nodes, extending known results from compact domains.
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.