Construction of Hermite subdivision schemes reproducing polynomials

Byeongseon Jeong, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The aim of this study is to present a new class of quasi-interpolatory Hermite subdivision schemes of order two with tension parameters. This class extends and unifies some of well-known Hermite subdivision schemes, including the interpolatory Hermite schemes. Acting on a function and the associated first derivative values, each scheme in this class reproduces polynomials up to a certain degree depending on the size of stencil. This is desirable property since the reproduction of polynomials up to degree d leads to the approximation order d+1. The smoothness analysis has been performed by using the factorization framework of subdivision operators. Lastly, we present some numerical examples to demonstrate the performance of the proposed Hermite schemes.

Original languageEnglish
Pages (from-to)565-582
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume451
Issue number1
DOIs
StatePublished - 1 Jul 2017

Keywords

  • Convergence
  • Hermite subdivision scheme
  • Polynomial reproduction
  • Quasi-interpolation
  • Smoothness
  • Spectral condition

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