D.E. Roberts
A vector Chebysev algorithm.
Roberts, D.E.
Authors
Abstract
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.
Citation
Roberts, D. (1998). A vector Chebysev algorithm. Numerical Algorithms, 17(1/2), 33-50. https://doi.org/10.1023/A%3A1011633327892
Journal Article Type | Article |
---|---|
Publication Date | 1998-05 |
Deposit Date | Oct 1, 2008 |
Publicly Available Date | Oct 1, 2008 |
Print ISSN | 1017-1398 |
Electronic ISSN | 1572-9265 |
Publisher | BMC |
Peer Reviewed | Peer Reviewed |
Volume | 17 |
Issue | 1/2 |
Pages | 33-50 |
DOI | https://doi.org/10.1023/A%3A1011633327892 |
Keywords | Clifford algebras; Orthogonal polynomials; Quotient-difference algorithm; Chebyshev algorithm; Vector Pad´e approximants; Designants. |
Public URL | http://researchrepository.napier.ac.uk/id/eprint/2425 |
Contract Date | Oct 1, 2008 |
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