Weighted discrete least-squares polynomial approximation using randomized quadratures

doi:10.1016/j.jcp.2015.06.042

	Weighted discrete least-squares polynomial approximation using randomized quadratures
	Zhou, Tao1 ; Narayan, Akil 2,3; Xiu, Dongbin 2,3
	2015-10-01
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	298 页码:787-800
摘要	We discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation. The problem stems from uncertainty quantification (UQ), where the independent variables of the functions are random variables with specified probability measure. We propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product Gaussian quadrature points. We analyze the stability properties of this method and prove that the method is asymptotically stable, provided that the number of points scales linearly (up to a logarithmic factor) with the cardinality of the polynomial space. Specific results in both bounded and unbounded domains are obtained, along with a convergence result for Chebyshev measure. Numerical examples are provided to verify the theoretical results. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Least squares method Orthogonal polynomials Generalized polynomial chaos Uncertainty quantification
DOI	10.1016/j.jcp.2015.06.042
语种	英语
资助项目	National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11201461] ; AFOSR[FA95501410022] ; AFOSR[DOE DESC0011615] ; NSF[1418771] ; NSF[1318427]
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000358796700044
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/20484
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.Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, Beijing, 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
推荐引用方式 GB/T 7714	Zhou, Tao,Narayan, Akil,Xiu, Dongbin. Weighted discrete least-squares polynomial approximation using randomized quadratures[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2015,298:787-800.
APA	Zhou, Tao,Narayan, Akil,&Xiu, Dongbin.(2015).Weighted discrete least-squares polynomial approximation using randomized quadratures.JOURNAL OF COMPUTATIONAL PHYSICS,298,787-800.
MLA	Zhou, Tao,et al."Weighted discrete least-squares polynomial approximation using randomized quadratures".JOURNAL OF COMPUTATIONAL PHYSICS 298(2015):787-800.