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Roberts, David E (1998) A vector Chebysev algorithm. Numerical algorithms, 17 (1-2). pp. 33-50. ISSN 10171398
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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 |
|---|---|
| Print ISSN: | 10171398 |
| Electronic ISSN: | 15729265 |
| Additional Information: | The original publication is available at http://www.springerlink.com |
| 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: | 12 Jan 2011 04:49 |
| URI: | http://researchrepository.napier.ac.uk/id/eprint/2425 |
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