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.

  • Type:

    Article

  • Date:

    30 April 1998

  • Publication Status:

    Published

  • Publisher

    Springer

  • DOI:

    10.1023/A:1011633327892

  • ISSN:

    1017-1398

  • Library of Congress:

    QA Mathematics

  • Dewey Decimal Classification:

    512 Algebra

Citation

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

Keywords

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

Available Documents