Weighted Fej\'er Constants and Fekete Sets

TL;DR

This paper explores the relationships between Fekete sets, orthogonal polynomial zeros, and interpolation nodes through Fejér constants, and proves convergence of a weighted Grünwald interpolation method.

Contribution

It establishes connections among various mathematical concepts and demonstrates the convergence of a specific weighted interpolation technique.

Findings

Connections among Fekete sets, orthogonal polynomial zeros, and interpolation nodes are established.

Convergence of a weighted Grünwald interpolation method is proved.

Abstract

We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fej\'er contants. Finally the convergence of a weighted Gr\"unwald interpolation is proved.