Hermite interpolation property is desired in applied and computational mathematics. Hermite and vector subdivision schemes are of interest in CAGD for generating subdivision curves and in computational mathematics for building Hermite wavelets to numerically solve partial differential equations. In contrast to well-studied scalar subdivision schemes, Hermite and vector subdivision schemes employ matrix-valued masks and vector input data, which make their analysis much more complicated and difficult than their scalar counterparts. Despite recent progresses on Hermite subdivision schemes, several key questions still remain unsolved, for example, characterization of Hermite masks, factorization of matrix-valued masks, and convergence of Hermite subdivision schemes. In this paper, we shall study Hermite subdivision schemes through investigating vector subdivision operators acting on vector polynomials and establishing the relations among Hermite subdivision schemes, vector cascade algorithms and refinable vector functions. This approach allows us to resolve several key problems on Hermite subdivision schemes including characterization of Hermite masks, factorization of matrix-valued masks, and convergence of Hermite subdivision schemes.

翻译：在应用和计算数学方面,热量和矢量分层计划是理想的,在应用和计算数学方面,热量和矢量分层计划是符合CAGD的,因为CAGD生成了亚形曲线,在建立Hermite波浪以量化解决部分差异方程式的计算数学方面,热量和矢量分层计划与经过充分研究的标量分层计划相反,Hermite和矢量分层计划采用矩阵价值的遮罩和矢量输入数据,这使得其分析比标度分层计划更加复杂和困难得多。尽管最近在Hermite分层计划方面取得了进展,但一些关键问题仍未解决,例如,Hermite面具的定性、矩阵价值面罩的因子化以及Hermite亚形图层组合。在本文件中,我们将研究Hermite子分层计划,通过调查病媒分层操作者在矢量聚度上采取行动,建立Hermite亚层系统、病媒级算法和可修复的矢量函数之间的关系。这一方法使我们得以解决Hermite分层分层计划的若干关键问题,包括Hermite面面面面面面图的特征的特征、矩阵组合的趋同化因素。