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 |
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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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