On computational aspects of discrete Sobolev inner products on the unit circle

Kenier Castillo, Lino G. Garza, Francisco Marcellán

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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. © 2013 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)452-460
Number of pages9
JournalApplied Mathematics and Computation
DOIs
Publication statusPublished - 17 Sep 2013
Externally publishedYes

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Sobolev Inner Products
Unit circle
Discrete Orthogonal Polynomials
Polynomials
Sobolev Orthogonal Polynomials
Fourier coefficients
Orthogonality
Unit Disk
Deduce
Derivatives
Derivative
Closed
Polynomial

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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On computational aspects of discrete Sobolev inner products on the unit circle. / Castillo, Kenier; Garza, Lino G.; Marcellán, Francisco.

In: Applied Mathematics and Computation, 17.09.2013, p. 452-460.

Research output: Contribution to journalArticle

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