Analysis of the Gibbs phenomenon in stationary subdivision schemes

Journal ar
Applied Mathematics Letters
  • Volumen: 76
  • Fecha: 01 February 2018
  • Páginas: 157-163
  • ISSN: 18735452 08939659
  • Source Type: Journal
  • DOI: 10.1016/j.aml.2017.08.014
  • Document Type: Article
  • Publisher: Elsevier Ltd
© 2017 Elsevier Ltd In this paper sufficient conditions to determine if a stationary subdivision scheme produces Gibbs oscillations close to discontinuities are presented. It consists of the positivity of the partial sums of the values of the mask. We apply the conditions to non-negative masks and analyze (numerically when the sufficient conditions are not satisfied) the Gibbs phenomenon in classical and recent subdivision schemes like B-splines, Deslauriers and Dubuc interpolation subdivision schemes and the schemes proposed in Siddiqi and Ahmad (2008).

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