2006/02/18 by Sobczyk, Garret
#13F10 #13F20 #15A24 #41A10 #41A15 #41A20 #41A21 #65D05 #65D07 #65D17 #FOS: Mathematics #Numerical Analysis (math.NA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.math/0602405
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.