Vector continued fraction algorithms.

Roberts, D. E.

Abstract

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 the vector elements of these fractions have been established using Clifford algebras. We devise new algorithms based on these which involve operations on vectors and scalars only — a desirable characteristic for computations involving vectors of large dimension. As a consequence, we are able to form new expressions for the numerator and denominator polynomials of these approximants as products of vectors, thus retaining their Clifford nature.

Citation

Roberts, D. E. (1996). Vector continued fraction algorithms. In R. Ablamowicz, P. Lounesto, & J. M. Parra (Eds.), Clifford algebras with numeric and symbolic computations (111-119). Birkhauser Verlag AG. https://doi.org/10.1007/978-1-4615-8157-4_7

• Publication Date: 1996-05
• Deposit Date: Oct 1, 2008
• Publicly Available Date: Oct 1, 2008
• Peer Reviewed: Peer Reviewed
• Pages: 111-119
• Book Title: Clifford algebras with numeric and symbolic computations.
• ISBN: 0817639071 or 9780817639075
• DOI: https://doi.org/10.1007/978-1-4615-8157-4_7
• Keywords: Vector Pade approximants; Power series; Continued fractions; Rational approximants; Viskovatov; Modified Euclidean algorithm; Clifford algebra.
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/2427
• Contract Date: Oct 1, 2008