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Author:   Sergiy V. Borodachov ,  Douglas P. Hardin ,  Edward B. Saff
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. 2019
Weight:   1.184kg
ISBN:  

9780387848075

ISBN 10:   038784807
Pages:   666
Publication Date:   01 November 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

"0. An Overview: Discretizing Manifolds via Particle Interactions.-1. Preliminaries.- 2. Basics of Minimal Energy.- 3.-Introduction to Packing and Covering.- 4. Continuous and Discrete Energy.- 5. LP Bounds on the Sphere.- 6. Asymptotics for Energy Minimizing Congurations on Sd.- 7. Some Popular Algorithms for Distributing Points on S2.- 8. Minimal Energy in the Hypersingular Case.-  9. Minimal Energy Asymptotics in the ""Harmonic Series"" Case.-  10. Periodic Riesz Energy.- 11. Congurations with non-Uniform Distribution.-  12. Low Complexity Energy Methods for Discretization.- 13. Best-Packing on Compact Sets.- 14. Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants.- Appendix.- References.- List of Symbols.- Index."

Reviews

The authors have done an excellent work by taking the reader, who is primarily supposed to be a graduate student, from the basics of Real Analysis to the frontiers of research on several mathematical topics, what turns the text of interest for both students and research professionals. The vast content of the book will certainly provide the reader with an extremely valuable source on this fascinating subject. (Antonio Roberto da Silva, zbMATH 1437.41002, 2020)

Author Information

Sergiy V. Borodachov is a Professor of Mathematics at Towson University, which he joined in 2008. Prof. Borodachov's primary research interests include approximation theory, numerical analysis, and minimal energy problems. He authored or co-authored more than 30 research articles and gave more than 90 talks at research conferences and seminars. Douglas P. Hardin is a Professor of Mathematics and a Professor of Biomedical Informatics at Vanderbilt University.  His research interests include discrete minimum energy problems, fractals, harmonic analysis (wavelets), inverse problems, and machine learning.  Hardin has authored or co-authored over 115 research publications, 2 monographs, and co-edited 3 research journal special issues. Edward B. Saff is a Professor of Mathematics at Vanderbilt University and Director of the Center for Constructive Approximation. His research areas include approximation theory, numerical analysis, and potential theory. Saff is a Fellow of the American Mathematics Society, a Foreign Member of the Bulgarian Academy of Science, and was a recipient of both a Guggenheim and a Fulbright Fellowships. He has authored or co-authored over 270 research articles, 4 research monographs and 4 textbooks, and is co-Editor-in-Chief and Managing Editor of the research journal Constructive Approximation. Prof. Saff also serves on the boards of 3 other research journals.  

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