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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 Padé approximants.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
The aim of this paper is to define and to study orthogonal polynomials with respect to a linear functional whose moments are
vectors. We show how a Clifford algebra allows us to construct such polynomials in a natural way. This new definition is motivated
by the fact that there exist natural links between this theory of orthogonal polynomials and the theory of the vector valued
Padé approximants in the sense of Graves-Morris and Roberts.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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