KMS Of Academy of mathematics and systems sciences, CAS
Weighted discrete least-squares polynomial approximation using randomized quadratures | |
Zhou, Tao1; Narayan, Akil2,3; Xiu, Dongbin2,3 | |
2015-10-01 | |
Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS |
ISSN | 0021-9991 |
Volume | 298Pages:787-800 |
Abstract | 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. |
Keyword | Least squares method Orthogonal polynomials Generalized polynomial chaos Uncertainty quantification |
DOI | 10.1016/j.jcp.2015.06.042 |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11201461] ; AFOSR[FA95501410022] ; AFOSR[DOE DESC0011615] ; NSF[1418771] ; NSF[1318427] |
WOS Research Area | Computer Science ; Physics |
WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
WOS ID | WOS:000358796700044 |
Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/20484 |
Collection | 计算数学与科学工程计算研究所 |
Affiliation | 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 |
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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