Multivariate splines and polytopes
文献类型：期刊论文
| 作者 | Xu, Zhiqiang
|
| 刊名 | JOURNAL OF APPROXIMATION THEORY
 |
| 出版日期 | 2011-03-01 |
| 卷号 | 163期号:3页码:377-387 |
| 关键词 | Box splines Multivariate truncated powers Polytopes Unit cubes |
| ISSN号 | 0021-9045 |
| DOI | 10.1016/j.jat.2010.10.005 |
| 英文摘要 | In this paper, we use multivariate splines to investigate the volume of polytopes. We first present an explicit formula for the multivariate truncated power, which can be considered as a dual version of the famous Brion's formula for the volume of polytopes. We also prove that the integration of polynomials over polytopes can be dealt with by using the multivariate truncated power. Moreover, we show that the volume of cube slicing can be considered as the maximum value of the box spline. On the basis of this connection, we give a simple proof for Good's conjecture, which has been settled before by probability methods. (C) 2010 Elsevier Inc. All rights reserved. |
| 语种 | 英语 |
| WOS记录号 | WOS:000287910600006 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/12454]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Xu, Zhiqiang |
| 作者单位 | Chinese Acad Sci, Inst Computat Math, Acad Math & Syst Sci, LSEC, Beijing 100091, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Zhiqiang. Multivariate splines and polytopes[J]. JOURNAL OF APPROXIMATION THEORY,2011,163(3):377-387. |
| APA | Xu, Zhiqiang.(2011).Multivariate splines and polytopes.JOURNAL OF APPROXIMATION THEORY,163(3),377-387. |
| MLA | Xu, Zhiqiang."Multivariate splines and polytopes".JOURNAL OF APPROXIMATION THEORY 163.3(2011):377-387. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。