Optimal configurations of lines and a statistical application

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• 作者：François Bachoc ; Martin Ehler ; Manuel Gräf
• 关键词：Projective space ; Potential energy ; Universal optimality ; Confidence intervals
• 刊名：Advances in Computational Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：43
• 期：1
• 页码：113-126
• 全文大小：443KB
• 刊物类别：Computer Science
• 刊物主题：Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics; Mathematical and Computational Biology; Computational Science and Engineering; Visualization;
• 出版者：Springer US
• ISSN：1572-9044
• 卷排序：43

文摘

Motivated by the construction of confidence intervals in statistics, we study optimal configurations of 2d − 1 lines in real projective space ℝℙd−1. For small d, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of 2d − 1 lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature.