Computing recursive orthogonal polynomial with Schur complements

[摘要] In the present paper, we give the expression of orthogonal polynomials as Schur complements. We use the Schur complement and its properties to get a recurrence relation between two families of orthogonal polynomials. We derive two recursive algorithms for computing the orthogonal polynomials by using the qd algorithm and the well known recurrence relation of Hankel determinants. We also give a useful recurrence relation between the orthogonal polynomials of the same family and auxiliary polynomials, which allows us to build a third algorithm for computing recursively the orthogonal polynomials. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2020-08-01

[效力级别]  Proceedings Paper

[关键词] Orthogonal polynomials;Schur complement;Sylvester's identity;Recursive orthogonal polynomial algorithm;Qd algorithm