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Regular version of the site

Article

Regularity of non-stationary subdivision: a matrix approach

Numerische Mathematik. 2017. Vol. 135. No. 3. P. 639-678.
Protasov V. Y., Conti C., Charina M., Guglielmi N.

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 ≥ 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.