WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION

doi:10.1137/17M1140960

	WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION
	Guo, Ling 1; Narayan, Akil 2,3; Yan, Liang 4; Zhou, Tao5
	2018
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	40 期号:1 页码:A366-A387
摘要	We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations on L-2 spaces weighted by a probability density function. Our procedure is a particular weighted version of the approximate Fekete points method, with the weight function chosen as the (inverse) Christoffel function. Our procedure has theoretical advantages: when linear systems with optimal condition number exist, the procedure finds them. In the one-dimensional setting with any density function, our greedy procedure almost always generates optimally conditioned linear systems. Our method also has practical advantages: our procedure is impartial to the compactness of the domain of approximation and uses only pivoted linear algebraic routines. We show through numerous examples that our sampling design outperforms competing randomized and deterministic designs when the domain is both low and high dimensional.
关键词	uncertainty quantification least-squares approximations Fekete points QR decomposition
DOI	10.1137/17M1140960
语种	英语
资助项目	NSF of China[11671265] ; NSF of China[11771081] ; Program for Outstanding Academic Leaders in Shanghai City[151503100] ; AFOSR[FA9550-15-1-0467] ; DARPA EQUiPS[N660011524053] ; Qing Lan Project of Jiangsu Province ; Science Challenge Project[TZ2016001] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[91630312] ; National Natural Science Foundation of China[91630203] ; National Natural Science Foundation of China[11571351] ; National Natural Science Foundation of China[11731006] ; NCMIS ; Youth Innovation Promotion Association (CAS)
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000426743500016
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29892
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	1.Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China 2.Univ Utah, Dept Math, Salt Lake City, UT 84112 USA 3.Univ Utah, Sci Comp & Imaging Inst, Salt Lake City, UT 84112 USA 4.Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China 5.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Guo, Ling,Narayan, Akil,Yan, Liang,et al. WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2018,40(1):A366-A387.
APA	Guo, Ling,Narayan, Akil,Yan, Liang,&Zhou, Tao.(2018).WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION.SIAM JOURNAL ON SCIENTIFIC COMPUTING,40(1),A366-A387.
MLA	Guo, Ling,et al."WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION".SIAM JOURNAL ON SCIENTIFIC COMPUTING 40.1(2018):A366-A387.