Edinburgh Napier University

  Napier Report CAM 95-3 (1995)

We consider the construction of rational approximations to given power series whose coefficients are vectors. The approximants are in the form of vector-valued continued fractions which may be used to obtain vector Pade approximants using recurrence relations. Algorithms for the determination of these fractions have been established using Clifford algebras. We devise new algorithms based on these which involve only vectors and scalars — a desirable characteristic for computations involving vectors of large dimension. Finally, we present a novel use of Clifford algebras by suggesting a definition of approximant which reflects more faithfully the singularities of the given function