Lagrange interpolation at real projections of Leja sequences for the unit disk

TL;DR

This paper demonstrates that the Lebesgue constant for real projections of Leja sequences on the unit disk grows polynomially, enabling explicit multivariate interpolation points with similarly controlled growth.

Contribution

It introduces the first explicit construction of multivariate interpolation points in $[-1,1]^N$ with polynomial growth of the Lebesgue constant.

Findings

Lebesgue constant grows polynomially for real projections of Leja sequences

Constructs explicit multivariate interpolation points with polynomial Lebesgue constant growth

Provides new tools for multivariate polynomial interpolation in hypercubes

Abstract

We show that the Lebesgue constant of the real projection of Leja sequences for the unit disk grows like a polynomial. The main application is the first construction of explicit multivariate interpolation points in $[-1,1]^N$ whose Lebesgue constant also grows like a polynomial.