On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification

doi:10.1137/140961894

科研成果详情

发表状态	已发表Published
题名	On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification
作者	Tang, Tao1 ; Zhou, Tao 2
发表日期	2014
发表期刊	SIAM Journal on Scientific Computing
ISSN/eISSN	1064-8275
卷号	36 期号:5 页码:A2272–A2295
摘要	This work is concerned with approximating multivariate functions in an unbounded domain by using a discrete least-squares projection with random point evaluations. Particular attention is given to functions with random Gaussian or gamma parameters. We first demonstrate that the traditional Hermite (Laguerre) polynomials chaos expansion suffers from the instability in the sense that an unfeasible number of points, which is relevant to the dimension of the approximation space, is needed to guarantee the stability in the least-squares framework. We then propose to use the Hermite/Laguerre functions (rather than polynomials) as bases in the expansion. The corresponding design points are obtained by mapping the uniformly distributed random points in bounded intervals to the unbounded domain, which involved a mapping parameter L. By using the Hermite/Laguerre functions and a proper mapping parameter, the stability can be significantly improved even if the number of design points scales linearly (up to a logarithmic factor) with the dimension of the approximation space. Apart from the stability, another important issue is the rate of convergence. To speed up the convergence, an effective scaling factor is introduced, and a principle for choosing quasi-optimal scaling factor is discussed. Applications to parametric uncertainty quantification are illustrated by considering a random ODE model together with an elliptic problem with lognormal random input.
关键词	uncertainty quantification least-squares projection unbounded domain Hermite functions scaling stability
DOI	10.1137/140961894
URL	查看来源
收录类别	SCIE
语种	英语English
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000346123200008
引用统计	被引频次：29[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	https://repository.uic.edu.cn/handle/39GCC9TT/4793
专题	个人在本单位外知识产出
作者单位	1.Department of Mathematics, The Hong Kong Baptist University, Kowloon Tong, Kowloon, Hong Kong, China; 2.Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, The Chinese Academy of Sciences, Beijing, China
推荐引用方式 GB/T 7714	Tang, Tao,Zhou, Tao. On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification[J]. SIAM Journal on Scientific Computing, 2014, 36(5): A2272–A2295.
APA	Tang, Tao, & Zhou, Tao. (2014). On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification. SIAM Journal on Scientific Computing, 36(5), A2272–A2295.
MLA	Tang, Tao,et al."On Discrete Least-Squares Projection in Unbounded Domain with Random Evaluations and its Application to Parametric Uncertainty Quantification". SIAM Journal on Scientific Computing 36.5(2014): A2272–A2295.