An Algorithm to Compute CVTs for Finitely Generated Cantor Distributions

Authors

Carl P. Dettmann
Mrinal Kanti Roychowdhury, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

2021

Abstract

Centroidal Voronoi tessellations (CVTs) are Voronoi tessellations of a region such that the generating points of the tessellations are also the centroids of the corresponding Voronoi regions with respect to a given probability measure. CVT is a fundamental notion that has a wide spectrum of applications in computational science and engineering. In this paper, an algorithm is given to obtain the CVTs with n-generators to level m, for any positive integers m and n, of any Cantor set generated by a pair of self-similar mappings given by S1(x)=r1x and S2(x)=r2x+(1−r2) for x∈R, where r1,r2>0 and r1+r20 and p1+p2=1.

Recommended Citation

Dettmann, C. P., and M. K. Roychowdhury. 2021. “An Algorithm to Compute CVTs for Finitely Generated Cantor Distributions.” Southeast Asian Bulletin of Mathematics 45 (3): 173–88.

Publication Title

Southeast Asian Bulletin of Mathematics