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One of the beauties of mathematics is that it can uncover connections between seemingly disparate applications. One of the most fertile grounds for unearthing connections is computational algorithms where one often discovers that an algorithm developed for one application is equally useful in several others. One such algorithm is centroidal Voronoi tessellations (CVTs) which are special Voronoi diagrams for which the generators of the diagrams are also the centers of mass (with respect to a given density function) of the Voronoi cells. CVTs have many uses and applications, several of which we discuss. These include data compression, image segmentation, clustering, cell biology, territorial behavior of animals, resource allocation, grid generation in volumes and on surfaces, meshless computing, hypercube sampling, and reduced-order modeling. We also discuss deterministic and probabilistic methods for determining CVTs.
Max Gunzburger is the Frances Eppes Professor of Computational Science and Mathematics at Florida State University. He received his Ph.D. degree from New York University and has held positions at the
University of Tennessee, Carnegie Mellon University, Virginia Tech, and Iowa State University. He was awarded an "Innovator's Prize for Inventions and Contributions" by NASA and a "Guest Professorship" by Peking University. He formerly served as Chairman the SIAM Board of Trustees. He serves as Editor in Chief of the SIAM Journal on
Numerical Analysis and on the editorial board of several other journals and book series. He is the author of five books and over 225 papers. His research interests include computational methods for partial differential equations, especially finite element methods in general and least-squares and stabilized finite element methods in particular, control of complex systems, reduced-order modeling, fluid
mechanics, superconductivity, data mining, computational geometry, image processing, uncertainty quantification, and numerical analysis.
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