Multidimensional intertwining Leja sequences and applications in bidimensional Lagrange interpolation

TL;DR

This paper introduces a method for constructing multidimensional Leja sequences from one-dimensional sequences and explores their applications in bidimensional Lagrange interpolation, including explicit formulas and uniform estimates.

Contribution

It presents a novel approach to generate multidimensional Leja sequences via intertwining one-dimensional sequences and applies these to bidimensional interpolation problems.

Findings

Explicit construction of multidimensional Leja sequences.

Application to bidimensional Lagrange interpolation.

Derivation of explicit formulas with uniform estimates.

Abstract

We first give a method to get multidimensional Leja sequences by considering intertwining sequences from one-dimensional ones. An application is the existence of explicit Leja sequences for the closed unit polydisc. Next, we deal with some applications in bidimensional Lagrange interpolation with intertwining Leja sequences. These results also require an explicit formula for the associated fundamental Lagrange polynomials with uniform estimates.