On a linear interpolation problem for n-dimensional vector polynomials
  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. 
Mikhail Kudryavtsev, Sergio Palafox, Luis O. Silva
math.CA