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

publication date

  • October 2013

start page

  • 452

end page

  • 460

issue

  • OCTUBRE

volume

  • 223

international standard serial number (ISSN)

  • 0096-3003

electronic international standard serial number (EISSN)

  • 1873-5649

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.

keywords

  • discrete sobolev inner product; gelfand-levitan approach; computational complexity; cholesky decomposition; outer relative asymptotics