The Spectral Basis and Rational Interpolation
arXiv:math/0602405
Abstract
The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Pade and other interpolation schemes. A unified view of these various interpolation techniques is eloquently expressed in terms of the concept of the spectral basis of a factor ring of polynomials. When these methods are applied to the minimal polynomial of a matrix, they give a family of rational forms of functions of that matrix.
8 pages, 2 figures