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Vector Continued Fraction Algorithms

In: Clifford Algebras with Numeric and Symbolic Computations

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  • D. E. Roberts

    (Napier University, Department of Mathematics)

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 Padé 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.

Suggested Citation

  • D. E. Roberts, 1996. "Vector Continued Fraction Algorithms," Springer Books, in: Rafał Abłamowicz & Josep M. Parra & Pertti Lounesto (ed.), Clifford Algebras with Numeric and Symbolic Computations, pages 111-119, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-8157-4_7
    DOI: 10.1007/978-1-4615-8157-4_7
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