Euclidean Design Theory

Covers the constructions of optimal experimental designs comprehensively

Provides a novel framework for understanding optimal designs, based on the theory of cubature formulas in analysis and spherical/Euclidean designs in combinatorics

Presents a fresh approach for introducing the theory of the cubature formula with reproducing kernel Hilbert space in functional analysis

Covers the constructions of optimal experimental designs comprehensively Provides a novel framework for understanding optimal designs, based on the theory of cubature formulas in analysis and spherical/Euclidean designs in combinatorics Presents a fresh approach for introducing the theory of the cubature formula with reproducing kernel Hilbert space in functional analysis

Autorentext

Masanori Sawa received his M.S. degree in Mathematics from Hiroshima University in 2005 and Ph.D. degree in Information Science from Nagoya University in 2007. He was a postdoctoral fellow with the Japan Society for the Promotion of Science, a lecturer at the Takamatsu National College of Technology, and an Assistant Professor at Nagoya University. He has been an Associate Professor at the Graduate School of System Informatics, Kobe University, Japan, since 2014. His current research interests include algebraic combinatorics, numerical analysis and mathematical statistics. Masatake Hirao received his M.S. and Ph.D. degrees in Information Science from Nagoya University, Japan, in 2006 and 2010, respectively. He has been an Associate Professor at the School of Information and Science Technology, Aichi Prefectural University, Japan, since 2014. His research interests are mathematical statistics, probability theory, combinatorics and numerical analysis.

Sanpei Kageyama has been a Visiting Professor of Statistics and Discrete Mathematics at the Research Center for Mathmatics and Science Education, Tokyo University of Science, Japan, since 2016. He is now an Emeritus Professor of Hiroshima University. He has published over 340 articles in scientific journals. He was a Foundation Fellow of the Institute of Combinatorics and its Applications, and a council member of the Mathematical Society of Japan, the Japan Statistical Society, and Japanese Society of Applied Statistics. He has also served on the editorial boards of Utilitas Mathematics, Journal of Statistical Planning and Inference, Discussiones Mathematicae, Sankhya, and the Journal of Statistics and Applications.

Inhalt
Chapter I: Reproducing Kernel Hilbert Space.- Chapter II: Cubature Formula.- Chapter III: Optimal Euclidean Design.- Chapter IV: Constructions of Optimal Euclidean Design.- Chapter V: Euclidean Design Theory.