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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Liu, Jing"],"institution":null,"degree_name":"M.A.","degree_level":"Campus Access Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Lili Ju"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010-01-01T08:00:00Z","date_published":"2010-01-01T08:00:00Z","updated_at":"2026-07-24T04:37:14Z","subjects":["Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["© 2010, Jing Liu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarcommons.sc.edu/etd/364","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Lili Ju"]},{"key":"dc:creator","label":"Author","values":["Liu, Jing"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Access Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.A."]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["© 2010, Jing Liu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarcommons.sc.edu/etd/364"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions"]}]}],"canonical_facts":{"dc:contributor":["Lili Ju"],"dc:creator":["Liu, Jing"],"dc:description.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.
"],"dc:identifier":["https://scholarcommons.sc.edu/etd/364"],"dc:rights":["© 2010, Jing Liu"],"dc:subject":["Mathematics","Physical Sciences and Mathematics"],"dc:title":["Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Access Thesis"],"thesis:degree_name":["M.A."]},"updated_at":"2026-07-24T04:37:14Z"}