A piecewise polynomial approach to analyzing interpolatory subdivision

详细信息    查看全文

• 作者：Michael S.  ; Floater^a ; &#xA0 ; ^{michaelf@ifi.uio.no}
• 关键词：Interpolatory subdivision ; Piecewise polynomials
• 刊名：Journal of Approximation Theory
• 出版年：2011
• 出版时间：November 2011
• 年：2011
• 卷：163
• 期：11
• 页码：1547-1563
• 全文大小：300 K

文摘

The four-point interpolatory subdivision scheme of Dubuc and its generalizations to irregularly spaced data studied by Warren and by Daubechies, Guskov, and Sweldens are based on fitting cubic polynomials locally. In this paper, we analyze the convergence of the scheme by viewing the limit function as the limit of piecewise cubic functions arising from the scheme. This allows us to recover the regularity results of Daubechies et al.?in a simpler way and to obtain the approximation order of the scheme and its first derivative.