In this paper, we show how to compute in O( n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product.
Bibliographical noteFunding Information:
We are grateful to the anonymous referees for useful suggestions and comments. The research of K. Castillo was supported by CNPq Program/Young Talent Attraction, Ministério da Ciência, Tecnologia e Inovação of Brazil, Project 370291/2013-1. The research of K. Castillo and F. Marcellán was supported by Dirección General de Investigación, Ministerio de Economía y Competitividad of Spain , Grant MTM2012-36732-C03-01 . F. Marcellán also acknowledges the financial support of CAPES Program/Special Visiting Researcher by Ministério da Educação of Brasil, Project 107/2012
Copyright 2013 Elsevier B.V., All rights reserved.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics