Analysis of non-stationary Hermite subdivision schemes reproducing exponential polynomials

Byeongseon Jeong, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The aim of this paper is to study the convergence and smoothness of non-stationary Hermite subdivision schemes of order 2. In Conti et al. (2017) provided sufficient conditions for the convergence of a non-stationary Hermite subdivision scheme that reproduces a set of functions including exponential polynomials. The analysis has been focused on the non-stationary Hermite scheme with the order ≥3, but the case of 2 (which is practically most useful) is yet to be investigated. In this regard, the first goal of this paper is to fill the gap. We analyze the convergence of non-stationary Hermite subdivision schemes of order 2. Next, we provide a tool which allows us to estimate the smoothness of a non-stationary Hermite scheme by developing a novel factorization framework of non-stationary vector subdivision operators. Using the proposed non-stationary factorization framework, we estimate the smoothness of the non-stationary Hermite subdivision schemes: the non-stationary interpolatory Hermite scheme proposed by Conti et al., (2015) and a new class of non-stationary dual Hermite subdivision schemes of de Rham-type.

Original languageEnglish
Pages (from-to)452-469
Number of pages18
JournalJournal of Computational and Applied Mathematics
Volume349
DOIs
StatePublished - 15 Mar 2019

Keywords

  • Convergence
  • Exponential polynomial reproduction
  • Hermite subdivision scheme
  • Smoothness
  • Spectral condition
  • Taylor scheme

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