Date of Award

2010

Document Type

Campus Access Thesis

Department

Mathematics

First Advisor

Lili Ju

Abstract

A Voronoi tessellation whose generating points coincide with the centroids (mass centers) of the corresponding Voronoi regions is called a centroidal Voronoi tessellation (CVT). Due to the natural optimization properties enjoyed by CVTs, they have diverse applications in many areas of science and engineering. In this paper, we present a new algorithm for computing CVTs--the conjugate gradient method based on trust regions (CGTR). This algorithm significantly speeds up the computation of CVTs. Numerical experiments are also conducted to substantiate theoretical analysis.

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