Numerical Analysis Seminar

Date: October 18, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Peter Jantsch, TAMU

Title: The Lebesgue Constant for Leja Points on Unbounded Domains

Abstract: 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 $w : R \rightarrow [0, 1]$. Due to a simple recursive formulation, such abcissas show promise as 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.