Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations

Weak Global Convergence of the Lloyd Method for Computing Centroidal Voronoi Tessellations in R

Acceleration schemes for computing centroidal Voronoi tessellations

Centroidal Voronoi tessellations (CVT) have diverse applications in many areas of science and engineering. The development of e cient 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 anal...

Nondegeneracy and Weak Global Convergence of the Lloyd Algorithm in R

Abstract. Lloyd algorithm originated in the context of optimal quantization and represents a fixed point iteration for computing an optimal quantizer. Reducing average distortion at every step, it constructs a Voronoi partition of the domain and replaces each generator with the centroid of the corresponding Voronoi cell. Optimal quantization is obtained in the case of a centroidal Voronoi tesse...

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations

In this paper the numerical approximations of the GinzburgLandau model for a superconducting hollow spheres are constructed using a gauge invariant discretization on spherical centroidal Voronoi tessellations. A reduced model equation is used on the surface of the sphere which is valid in the thin spherical shell limit. We present the numerical algorithms and their theoretical convergence as we...

Anisotropic Centroidal Voronoi Tessellations and Their Applications

In this paper, we introduce a novel definition of the anisotropic centroidal Voronoi tessellation (ACVT) corresponding to a given Riemann metric tensor. A directional distance function is used in the definition to simplify the computation. We provide algorithms to approximate the ACVT using the Lloyd iteration and the construction of anisotropic Delaunay triangulation under the given Riemannian...