A class of C 2 quasi-interpolating splines free of Gibbs phenomenon

Sergio Amat, David Levin, Juan Ruiz-Álvarez, Juan C. Trillo, Dionisio F. Yáñez

Research output: Contribution to journalArticlepeer-review

Abstract

In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good candidates having C2 regularity. On the other hand, if the data points present discontinuities, the classical spline approximations produce Gibbs oscillations. In a recent paper, we have introduced a new nonlinear spline approximation avoiding the presence of these oscillations. Unfortunately, this new reconstruction loses the C2 regularity. This paper introduces a new nonlinear spline that preserves the regularity at all the joint points except at the end points of an interval containing a discontinuity, and that avoids the Gibbs oscillations.

Original languageEnglish
Pages (from-to)51-79
Number of pages29
JournalNumerical Algorithms
Volume91
Issue number1
DOIs
StatePublished - Sep 2022

Keywords

  • Adaption to discontinuities
  • C regularity
  • Computer aided design (modeling of curves)
  • Quasi-interpolation
  • Splines

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