Roberts, David E (1998) A vector Chebysev algorithm. Numerical algorithms, 17 (1-2). pp. 33-50. ISSN 10171398
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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.
|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|
|Depositing User:||Dr. David A. Cumming|
|Date Deposited:||01 Oct 2008 17:30|
|Last Modified:||12 Jan 2011 04:49|
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