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Of all publications in the section: 2
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Article
Charina M., Conti C., Guglielmi N. et al. Numerische Mathematik. 2016. P. 1-40.

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.

Added: Jul 1, 2016
Article
Protasov V. Y., Conti C., Charina M. et al. Numerische Mathematik. 2017. Vol. 135. No. 3. P. 639-678.

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.

Added: Feb 7, 2018