一个带参数的对偶插值型细分
A Parametric Dual Interpolatory Subdivision
DOI: 10.12677/PM.2024.142066, PDF,    国家自然科学基金支持
作者: 亓万锋*, 曹 宏, 何 月, 刘 月：辽宁师范大学数学学院，辽宁 大连
关键词: 细分格式；连续性；多项式再生性；H?lder指数；Subdivision Scheme； Continuity； Polynomial Reproduction； H?lder Exponent
摘要: 对偶插值型细分是近年来提出的一种新型细分格式。它区别于传统的插值型细分格式，不通过逐步插值的方式，而只是确保极限曲线插值于原始控制网格。对偶插值型细分可有效结合了插值型细分和对偶型细分的优势。由于其新颖性，该类格式引起了广泛的学术关注。本文提出了一个带参数的四重九点对偶插值型细分格式，对其连续性和多项式再生性进行了分析，并计算了相应的Hӧlder指数。
Abstract: The dual interpolatory subdivision, a novel subdivision scheme introduced in recent years, dis-tinguishes itself from traditional interpolatory subdivision schemes. Instead of employing a step-wise interpolation approach, it interpolates the limit curve to the original control mesh. This dual interpolatory subdivision effectively amalgamates the advantages of both interpolatory schemes and dual schemes. Owing to its innovative nature, this format has garnered widespread academic interest. This paper presents a parametric quaternary nine-point dual interpolatory subdivision scheme, analyzes its continuity and polynomial reproduction properties, and calculates the cor-responding Hӧlder exponent.
文章引用：亓万锋, 曹宏, 何月, 刘月. 一个带参数的对偶插值型细分[J]. 理论数学, 2024, 14(2): 661-668. https://doi.org/10.12677/PM.2024.142066

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