A vector Chebysev algorithm.

Roberts, D.E.

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