Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials

TL;DR

This paper demonstrates that gradient flows linked to Morse functions for symmetric continuous Hahn and Wilson polynomials converge exponentially to their roots, with symmetry reduction enhancing convergence rates.

Contribution

It introduces a new analysis of gradient flows for these polynomials and compares convergence behaviors, improving understanding of root-finding dynamics.

Findings

Gradient flows converge exponentially to polynomial roots.

Symmetry reduction improves convergence rates.

Comparison clarifies differences between Hahn and Wilson polynomial flows.

Abstract

We show that the gradient flows associated with a recently found family of Morse functions converge exponentially to the roots of the symmetric continuous Hahn polynomials. By symmetry reduction the rate of the exponential convergence can be improved, which is clarified by comparing with corresponding gradient flows for the roots of the Wilson polynomials.