KMS Of Academy of mathematics and systems sciences, CAS
| WEIGHTED APPROXIMATE FEKETE POINTS: SAMPLING FOR LEAST-SQUARES POLYNOMIAL APPROXIMATION | |
Guo, Ling1; Narayan, Akil2,3; Yan, Liang4; Zhou, Tao5
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| 2018 | |
| Source Publication | SIAM JOURNAL ON SCIENTIFIC COMPUTING
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| ISSN | 1064-8275 |
| Volume | 40Issue:1Pages:A366-A387 |
| Abstract | 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. |
| Keyword | uncertainty quantification least-squares approximations Fekete points QR decomposition |
| DOI | 10.1137/17M1140960 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000426743500016 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/29892 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Zhou, Tao |
| Affiliation | 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 |
| 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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