Abstract
AbstractIt is well known that Sobolev-type orthogonal polynomials with respect to measures supported on the real line satisfy higher-order recurrence relations and these can be expressed as a (2N + 1)-banded symmetric semi-infinite matrix. In this paper, we state the connection between these (2N + 1)-banded matrices and the Jacobi matrices associated with the three-term recurrence relation satisfied by the standard sequence of orthonormal polynomials with respect to the 2-iterated Christoffel transformation of the measure.
Funder
Comunidad de Madrid
Ministerio de Ciencia, Innovación y Universidades
Universidad de Alcalá
Publisher
Springer Science and Business Media LLC
Reference29 articles.
1. Alfaro, M., Marcellán, F., Rezola, M.L., Ronveaux, A.: On orthogonal polynomials of Sobolev type: algebraic properties and zeros. SIAM J. Math. Anal. 23(3), 737–757 (1992)
2. Bueno, M.I., Marcellán, F.: Darboux transformation and perturbation of linear functionals. Linear Algebra Appl. 384, 215–242 (2004)
3. Bueno, M.I., Marcellán, F.: Polynomial perturbations of bilinear functionals and Hessenberg matrices. Linear Algebra Appl. 414, 64–83 (2006)
4. Buhmann, M.D., Iserles, A.: On orthogonal polynomials transformed by the QR algorithm. J. Comput. Appl. Math. 43(1–2), 117–134 (1992)
5. Chihara, T.S.: An introduction to orthogonal polynomials. Mathematics and Its Applications Series. Gordon and Breach, New York (1978)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献