QD-algorithms and recurrence relations for biorthogonal polynomials

摘要

Biorthogonal polynomials Pn(i,j) include as particular cases vector orthogonal polynomials of dimension d and −d(d∈N). We pay special attention to the cases of dimension 1 and −1. We discuss the problem of computing Pn(i,j) using only one or several recurrence relations. Furthermore, we deduce all recurrence relations of a certain type that give Pn(i,j) from two other biorthogonal polynomials. The coefficients that appear in any two independent relations satisfy some identities from which it is possible to establish QD-like algorithms.