Joint spectral radius and ternary hermite subdivision
Joint spectral radius and ternary hermite subdivision
复制标题
联合谱半径和三元 Hermite 细分
DOI：
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发表时间：
2021
影响因子：
1.7
通讯作者：
Jean
中科院分区：
文献类型：
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作者：
M. Charina;C. Conti;Thomas Mejstrik;Jean
在本文中，我们构造了一族具有小支持度的一阶三值插值型Hermite细分格式，Hc2Documentclass[12pt]{Minimum}usepackage{amsath}usepackage{wa ysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathsfs}usepackage{upgreek}setlong{oddsidemarin}{-69pt}例如{Document}${mathscr{H}}Mathcal{C}^{2}$end{Document}-光滑性。实际上，离开二进制域，有可能得到比现有的二进制例子具有更高正则性的插值型Hermite细分格式。我们构造的模式族是一个两参数族，它的HC2Documentclass[12pt]{Minimum}usepackage{amsath}usepackage{wa ysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathsfs}usepackage{upgreek}setlong{oddsidemargin}{-69pt}例如in{Document}${mathscr{H}}mathcal{C}^{2}$end{Document}-只要参数是从某个多边形区域中选择的，就能保证光滑性。这一新族的构造灵感来自于Hassan和Dodgson对三值插值标量三点细分格式的几何洞察。利用联合谱半径技术证明了新Hermite格式的光滑性。
In this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and HC2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}${mathscr{H}}mathcal {C}^{2}$end{document}-smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose HC2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}${mathscr{H}}mathcal {C}^{2}$end{document}-smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.