Multivariate splines and polytopes

doi:10.1016/j.jat.2010.10.005

	Multivariate splines and polytopes
	Xu, Zhiqiang
	2011-03-01
发表期刊	JOURNAL OF APPROXIMATION THEORY
ISSN	0021-9045
卷号	163 期号:3 页码:377-387
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.
关键词	Box splines Multivariate truncated powers Polytopes Unit cubes
DOI	10.1016/j.jat.2010.10.005
语种	英语
资助项目	NSFC[10871196] ; NSFC[11021101] ; National Basic Research Program of China[2010CB832702]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000287910600006
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12455
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.