| 書目名稱 | Euclidean Design Theory | | 編輯 | Masanori Sawa,Masatake Hirao,Sanpei Kageyama | | 視頻video | http://file.papertrans.cn/317/316420/316420.mp4 | | 概述 | 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 spherica | | 叢書名稱 | SpringerBriefs in Statistics | | 圖書封面 |  | | 描述 | .This book is the modern first treatment of experimental designs, providing a comprehensive introduction to the interrelationship between the theory of optimal designs and the theory of cubature formulas in numerical analysis. It also offers original new ideas for constructing optimal designs.. . The book opens with some basics on reproducing kernels, and builds up to more advanced topics, including bounds for the number of cubature formula points, equivalence theorems for statistical optimalities, and the Sobolev Theorem for the cubature formula. It concludes with a functional analytic generalization of the above classical results.. . Although it is intended for readers who are interested in recent advances in the construction theory of optimal experimental designs, the book is also useful for researchers seeking rich interactions between optimal experimental designs and various mathematical subjects such as spherical designs in combinatorics and cubature formulas in numerical analysis, both closely related to embeddings of classical finite-dimensional Banach spaces in functional analysis and Hilbert identities in elementary number theory. Moreover, it provides a novel communicati | | 出版日期 | Book 2019 | | 關(guān)鍵詞 | Cubature Formula; Spherical Design; Euclidean Design; Optimal Design; Reproducing Kernel | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-13-8075-4 | | isbn_softcover | 978-981-13-8074-7 | | isbn_ebook | 978-981-13-8075-4Series ISSN 2191-544X Series E-ISSN 2191-5458 | | issn_series | 2191-544X | | copyright | The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019 |
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