Roberts, David E (1998) *A vector Chebysev algorithm.* Numerical algorithms, 17 (1-2). pp. 33-50. ISSN 1017 1398

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## Abstract/Description

We consider polynomials orthogonal relative to a sequence of vectors and derive their recurrence relations within the framework of Clifford algebras. We state sufficient conditions for the existence of a system of such polynomials. The coefficients in the above relations may be computed using a cross-rule which is linked to a vector version of the quotient-difference algorithm, both

of which are proved here using designants. An alternative route is to employ a vector variant of the Chebyshev algorithm. This algorithm is established and an implementation presented which does not require general Clifford elements. Finally, we comment on the connection with vector Pad´e approximants.

Item Type: | Article |
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Print ISSN: | 1017 1398 |

Electronic ISSN: | 1572 9265 |

Uncontrolled Keywords: | Clifford algebras; Orthogonal polynomials; Quotient-difference algorithm; Chebyshev algorithm; Vector Pad´e approximants; Designants. |

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: | 2425 |

Depositing User: | Dr. David A. Cumming |

Date Deposited: | 01 Oct 2008 17:30 |

Last Modified: | 18 Sep 2013 13:55 |

URI: | http://researchrepository.napier.ac.uk/id/eprint/2425 |

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