Analysis of non-stationary Hermite subdivision schemes reproducing exponential polynomials

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:349

Article; Proceedings Paper

Jeong, Byeongseon¹  Yoon, Jungho² 

[1] Ewha W Univ, Inst Math Sci, Seoul 120750, South Korea

[2] Ewha W Univ, Dept Math, Seoul 120750, South Korea

关键词: Hermite subdivision scheme;    Convergence;    Smoothness;    Exponential polynomial reproduction;    Spectral condition;    Taylor scheme;   

DOI  :  10.1016/j.cam.2018.07.050

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free