Regularity of non-stationary subdivision: a matrix approach

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• 作者：M. Charina ; C. Conti ; N. Guglielmi ; V. Protasov
• 关键词：Mathematics Subject Classification65D17 ; 15A60 ; 39A99
• 刊名：Numerische Mathematik
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：135
• 期：3
• 页码：639-678
• 全文大小：754KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Appl.Mathematics/Comput
• 出版者：Springer Berlin Heidelberg
• ISSN：0945-3245
• 卷排序：135

文摘

In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix M and present a unifying, general approach for checking their convergence and for determining their Hölder regularity (latter in the case \(M = mI, m \ge 2\)). The combination of the concepts of asymptotic similarity and approximate sum rules allows us to link stationary and non-stationary settings and to employ recent advances in methods for exact computation of the joint spectral radius. As an application, we prove a recent conjecture by Dyn et al. on the Hölder regularity of the generalized Daubechies wavelets. We illustrate our results with several examples.