论文标题
Hermite细分方案的分析和收敛
Analysis and convergence of Hermite subdivision schemes
论文作者
论文摘要
在应用和计算数学中，需要使用HERMITE插值属性。 HERMITE和矢量细分方案在CAGD中引起了人们的关注，用于生成细分曲线和计算数学，用于构建HERMITE小波以求解偏差方程。与研究良好的标量细分方案相反，Hermite和Vector细分方案采用了矩阵值掩膜和矢量输入数据，这使得与标量的分析更加复杂和困难。尽管最近在Hermite细分方案上取得了进展，但仍未解决的几个关键问题仍然没有解决，例如，Hermite面具的表征，基质值掩膜的分解以及Hermite细分方案的收敛。在本文中，我们应通过调查作用于矢量多项式的矢量细分操作员来研究Hermite细分方案，并建立Hermite细分方案之间的关系，矢量级联算法和可加固的矢量功能。这种方法使我们能够解决Hermite细分方案的几个关键问题，包括对HERMITE面具的表征，基质值掩膜的分解以及Hermite细分方案的收敛性。
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.
