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WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION
Guo, Ling1; Narayan, Akil2,3; Yan, Liang4; Zhou, Tao5
2018
Source PublicationSIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN1064-8275
Volume40Issue:1Pages:A366-A387
AbstractWe 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.
Keyworduncertainty quantification least-squares approximations Fekete points QR decomposition
DOI10.1137/17M1140960
Language英语
Funding ProjectNSF 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000426743500016
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29892
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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