Research Output
A vector Chebysev algorithm.
  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.

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  • Date:

    01 May 1998

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  • Library of Congress:

    QA Mathematics

  • Dewey Decimal Classification:

    512 Algebra


Roberts, D. (1998). A vector Chebysev algorithm. Numerical Algorithms, 17(1/2), (33-50). doi:10.1023/A:1011633327892. ISSN 1017-1398


Clifford algebras; Orthogonal polynomials; Quotient-difference algorithm; Chebyshev algorithm; Vector Pad´e approximants; Designants.

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