A new characterization of convergent multivariate subdivision schemes with nonnegative masks

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• 作者：Li Cheng ; Xinlong Zhou
• 关键词：Convergence ; Nonnegative mask ; Subdivision scheme
• 刊名：Archiv der Mathematik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：108
• 期：2
• 页码：197-207
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-8938
• 卷排序：108

文摘

We present in this paper new necessary and sufficient conditions for convergence of multivariate subdivision schemes with nonnegative finite masks, which simplify the assertion obtained by Wang in (J Approx Theory 113:207–220, 2001). Moreover, we construct an example, which shows that the convergence behaviors for univariate subdivision schemes and multivariate ones are essentially different.