Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2017;135(3):639-678.
doi: 10.1007/s00211-016-0809-y. Epub 2016 May 12.

Regularity of non-stationary subdivision: a matrix approach

M Charina  1 , C Conti  2 , N Guglielmi  3 , V Protasov  4
Affiliations

Regularity of non-stationary subdivision: a matrix approach

M Charina et al. Numer Math (Heidelb). 2017.

Abstract

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 [Formula: see text]). 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.

Keywords: 15A60; 39A99; 65D17.

PubMed Disclaimer

References

    1. Berger MA, Wang Y. Bounded semigroups of matrices. Linear Algebra Appl. 1992;166:21–27. doi: 10.1016/0024-3795(92)90267-E. - DOI
    1. Ben-Artzi A, Ron A. Translates of exponential box splines and their related spaces. Trans. Am. Math. Soc. 1988;309:683–710. doi: 10.1090/S0002-9947-1988-0961608-7. - DOI
    1. Burkhart D, Hamann B, Umlauf G. Iso-geometric finite element analysis based on Catmull-Clark subdivision solids. Comput. Graphics Forum. 2010;29:1575–1584. doi: 10.1111/j.1467-8659.2010.01766.x. - DOI
    1. Cabrelli CA, Heil C, Molter UM. Self-similarity and multiwavelets in higher dimensions. Mem. Am. Math. Soc. 2004;170(807):1–82.
    1. Cavaretta, A.S., Dahmen, W., Micchelli, C.A.: Stationary subdivision. Mem. Am. Math. Soc. 453, i-vi; 1–185 (1991)

LinkOut - more resources