On a linear interpolation problem for n-dimensional vector polynomials

TL;DR

This paper characterizes solutions to a linear interpolation problem for vector polynomials, generalizing rational interpolation results and applying to spectral analysis of band matrices.

Contribution

It provides a complete characterization of solutions for vector polynomial interpolation, extending previous rational interpolation results.

Findings

Generalizes rational interpolation to vector polynomials

Characterizes all solutions to the interpolation problem

Applications to spectral analysis of band matrices

Abstract

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear combination of them is satisfied for each one of the N interpolation nodes. The results of this work generalize previous results on the so-called rational interpolation and have applications to direct and inverse spectral analysis of band matrices.