QD-algorithms and
recurrence relations for biorthogonal polynomials
Abstract
Biorthogonal polynomials $P^{(i,j)}_{n}$
include as particular cases vector orthogonal polynomials of
dimension $d$ and $-d(d\in N)$. We pay special
attention to the cases of dimension 1 and -1.
We discuss the problem of computing
$P^{(i,j)}_{n}$ using only one of
several recurrence relations. Furthermore, we deduce all
recurrence relations of a certain type that give
$P^{(i,j)}_{n}$ from two others
biorthogonal polynomials. the coefficient that appear in any
two independents relations satisfy same identities from which
it is possible to establish QD-like algorithms.