  In this paper, motivated by applications in computer graphics and animation,
we study the numerical methods for checking $C^k-$regularity of vector
multivariate subdivision schemes with dilation 2I. These numerical methods
arise from the joint spectral radius and restricted spectral radius approaches,
which were shown in Charina (Charina, 2011) to characterize $W^k_p-$regularity
of subdivision in terms of the same quantity. Namely, the $(k,p)-$joint
spectral radius and the $(k,p)-$restricted spectral radius are equal. We show
that the corresponding numerical methods in the univariate scalar and vector
cases even yield the same upper estimate for the $(k,\infty)-$joint spectral
radius for a certain choice of a matrix norm. The difference between the two
approaches becomes apparent in the multivariate case and we confirm that they
indeed offer different numerical schemes for estimating the regularity of
subdivision. We illustrate our results with several examples.
