Decomposition of the infinite companion and interpolation Original Research Article

Formulae are given expressing the infinite companion matrix of a polynomial p as the sum of smaller matrices corresponding to the individual factors if p = p1 … pm. Connections with interpolation problems and partial fraction decompositions of rational functions are explained. The results are intended as a tool for representing Hankel matrices as sums of simpler Hankel matrices corresponding to the factors of the compatible polynomial. Explicit formulae are given for the inverse of the Chinese remainder operator and for the inverse of the confluent Vandermonde matrix.