On the characterization of the degree of interpolation polynomials in terms of certain combinatorical matrices

TL;DR

This paper links the degree of interpolation polynomials with the regularity of combinatorial matrices, providing a new characterization for equidistant base points.

Contribution

It introduces a novel characterization of interpolation polynomial degree using combinatorial matrix regularity, enhancing understanding of polynomial interpolation.

Findings

Degree of interpolation polynomial characterized by matrix regularity

Connection established between combinatorial matrices and interpolation degree

Provides a new perspective on polynomial interpolation with equidistant points

Abstract

In this note we show that the degree of the interpolation polynomial for equidistant base points is characterized by the regularity of matrices of combinatorical type.