Numerical methods for checking the regularity of subdivision schemes

Details Numerical methods for checking the regularity of subdivision schemes Numerical methods for checking the regularity of subdivision schemes

2012-02-10

arxiv.org/abs/1202.2765v1

Mathematics

Numerical Analysis

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Numerical methods for checking the regularity of subdivision schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Numerical methods for checking the regularity of subdivision schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical methods for checking the regularity of subdivision schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-276362