Centroidal Voronoi tessellations (CVT) have diverse applications in many areas of science and engineering. The development of efficient algorithms for their construction is a key to their success in practice. In this paper, we study some new algorithms for the numerical computation of the CVT, including the Lloyd–Newton iteration and the optimization based multilevel method. Both theoretical analysis and computational simulations are conducted. Rigorous convergence results are presented and significant speedup in computation is demonstrated through the comparison with traditional methods.
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Du et al. (2006) studied this question.
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