A vector Chebysev algorithm.

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

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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: 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: Users 10 not found.
Date Deposited: 01 Oct 2008 16:30
Last Modified: 18 Sep 2013 12:55

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