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Weighted discrete least-squares polynomial approximation using randomized quadratures
Zhou, Tao1; Narayan, Akil2,3; Xiu, Dongbin2,3
2015-10-01
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume298Pages:787-800
AbstractWe 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.
KeywordLeast squares method Orthogonal polynomials Generalized polynomial chaos Uncertainty quantification
DOI10.1016/j.jcp.2015.06.042
Language英语
Funding ProjectNational Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11201461] ; AFOSR[FA95501410022] ; AFOSR[DOE DESC0011615] ; NSF[1418771] ; NSF[1318427]
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000358796700044
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:16[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20484
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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