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Vector continued fraction algorithms.

Roberts, David E (1996) Vector continued fraction algorithms. In: Clifford algebras with numeric and symbolic computations. Birkhauser Verlag AG, pp. 111-119. ISBN 0817639071 or 9780817639075

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    Abstract/Description

    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.

    Item Type: Book Section
    ISBN: 0817639071 or 9780817639075
    Electronic ISBN: 978-1-4615-8157-4
    Uncontrolled Keywords: Vector Pade approximants; Power series; Continued fractions; Rational approximants; Viskovatov; Modified Euclidean algorithm; Clifford algebra.
    University Divisions/Research Centres: Faculty of Engineering, Computing and Creative Industries > School of Engineering and the Built Environment
    Dewey Decimal Subjects: 500 Science > 510 Mathematics > 512 Algebra
    Library of Congress Subjects: Q Science > QA Mathematics
    Item ID: 2427
    Depositing User: Dr. David A. Cumming
    Date Deposited: 01 Oct 2008 20:22
    Last Modified: 16 May 2014 14:03
    URI: http://researchrepository.napier.ac.uk/id/eprint/2427

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