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 = m I , 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.
Regularity of non-stationary subdivision: a matrix approach / Charina, Maria; Conti, Costanza; Guglielmi, Nicola; Protasov, Vladimir. - In: NUMERISCHE MATHEMATIK. - ISSN 0945-3245. - STAMPA. - 135:(2017), pp. 639-678. [10.1007/s00211-016-0809-y]
Regularity of non-stationary subdivision: a matrix approach
CONTI, COSTANZA;
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 M = m I , 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.File | Dimensione | Formato | |
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