On a representation of vector continued fractions.

Roberts, David E

Abstract

Vector Pade approximants to power series with vector coefficients may be calculated using the three-term recurrence relations of vector continued fractions
if formulated in the framework of Clifford algebras. We show that the numerator and denominator polynomials of these fractions take particularly simple forms which require just a few degrees of freedom in their representation. The new description also allows the calculation of ”hybrid” approximants.

Citation

Roberts, D. E. (1999). On a representation of vector continued fractions. Journal of Computational and Applied Mathematics, 105(1-2), 453-466. https://doi.org/10.1016/S0377-0427%2899%2900034-5

• Journal Article Type: Article
• Publication Date: 1999-05
• Deposit Date: Oct 2, 2008
• Publicly Available Date: Oct 2, 2008
• Print ISSN: 0377-0427
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 1-2
• Pages: 453-466
• DOI: https://doi.org/10.1016/S0377-0427%2899%2900034-5
• Keywords: Vector Pade approximants; Power series; Vector continued fractions; Clifford algebras; Lipschitz group; Recurrence relation; Hybrid approximants.
• Public URL: http://researchrepository.napier.ac.uk/id/eprint/2428
• Publisher URL: http://dx.doi.org/10.1016/S0377-0427(99)00034-5
• Contract Date: Oct 2, 2008