Weighted discrete least-squares polynomial approximation using randomized quadratures
文献类型：期刊论文
| 作者 | Zhou, Tao1 ; Narayan, Akil2,3; Xiu, Dongbin2,3
|
| 刊名 | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| 出版日期 | 2015-10-01 |
| 卷号 | 298页码:787-800 |
| 关键词 | Least squares method Orthogonal polynomials Generalized polynomial chaos Uncertainty quantification |
| ISSN号 | 0021-9991 |
| DOI | 10.1016/j.jcp.2015.06.042 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000358796700044 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20483]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。