Vector-valued Rational Interpolants II

Formulae for rational interpolation of vector data (in a spaceC^d]) at distinct points are given. Its confluent case of vector-valuedPadé approximation is shown to be equivalent to the Germanpolynomial approximation problem. Formulae are given for thevector of numerator polynomials and for the denominator polynomial.A continued fraction interpolant for vector data is also given.The methods are characterized by their requirement that certaindistinguished directions in the space C^d] form part of thespecification. The case of matrix Padé approximants forthe partial realization problem is explicitly discussed.