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

Kenier Castillo, Lino G. Garza, Francisco Marcellán

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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
Publication statusPublished - 17 Sep 2013
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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