Research Output

Vector continued fraction algorithms.

  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.

  • Type:

    Book Chapter

  • Date:

    30 April 1996

  • Publication Status:

    Published

  • Publisher

    Birkhauser Verlag AG

  • DOI:

    10.1007/978-1-4615-8157-4_7

  • Library of Congress:

    QA Mathematics

  • Dewey Decimal Classification:

    512 Algebra

Citation

Roberts, D. E. (1996). Vector continued fraction algorithms. In Ablamowicz, R., Lounesto, P. & Parra, J. M. (Eds.). Clifford algebras with numeric and symbolic computations., 111-119. Birkhauser Verlag AG. doi:10.1007/978-1-4615-8157-4_7. ISBN 0817639071 or 9780817639075

Keywords

Vector Pade approximants; Power series; Continued fractions; Rational approximants; Viskovatov; Modified Euclidean algorithm; Clifford algebra.

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