On the approximation properties of fast Leja points

TL;DR

This paper investigates the theoretical approximation properties of fast Leja points, demonstrating their potential effectiveness for Lagrange interpolation under certain asymptotic conditions.

Contribution

The paper introduces an asymptotic property of a triangular interpolation array and proves that fast Leja points are effective for Lagrange interpolation assuming this property.

Findings

Fast Leja points satisfy a specific asymptotic property.

Under this property, fast Leja points are proven to be suitable for Lagrange interpolation.

Theoretical foundation for the approximation capabilities of fast Leja points.

Abstract

Fast Leja points on an interval are points constructed using a discrete modification of the algorithm for constructing Leja points. Not much about fast Leja points has been proven theoretically. We present an asymptotic property of a triangular interpolation array, and under the assumption that fast Leja points satisfy this property, we prove that they are good for Lagrange interpolation.