A GENERALIZED SAMPLING AND PRECONDITIONING SCHEME FOR SPARSE APPROXIMATION OF POLYNOMIAL CHAOS EXPANSIONS

doi:10.1137/16M1063885

	A GENERALIZED SAMPLING AND PRECONDITIONING SCHEME FOR SPARSE APPROXIMATION OF POLYNOMIAL CHAOS EXPANSIONS
	Jakeman, John D.1; Narayan, Akil 2,3; Zhou, Tao4
	2017
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	39 期号:3 页码:A1114-A1144
摘要	We propose an algorithm for recovering sparse orthogonal polynomial expansions via collocation. A standard sampling approach for recovering sparse polynomials uses Monte Carlo sampling, from the density of orthogonality, which results in poor function recovery when the polynomial degree is high. Our proposed approach aims to mitigate this limitation by sampling with respect to the weighted equilibrium measure of the parametric domain and subsequently solves a preconditioned l(1)-minimization problem, where the weights of the diagonal preconditioning matrix are given by evaluations of the Christoffel function. Our algorithm can be applied to a wide class of orthogonal polynomial families on bounded and unbounded domains, including all classical families. We present theoretical analysis to motivate the algorithm and numerical results that show our method is superior to standard Monte Carlo methods in many situations of interest. Numerical examples are also provided to demonstrate that our proposed algorithm leads to comparable or improved accuracy even when compared with Legendre- and Hermite-specific algorithms.
关键词	uncertainty quantification polynomial chaos compressed sensing
DOI	10.1137/16M1063885
语种	英语
资助项目	U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program ; U.S. Department of Energy National Nuclear Security Administration[DE-AC04-94AL85000] ; DARPA EQUIPS ; AFOSR[FA9550-15-1-0467] ; DARPA[N660011524053] ; National Natural Science Foundation of China[91130003] ; National Natural Science Foundation of China[11571351]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000404763200026
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25934
专题	计算数学与科学工程计算研究所
通讯作者	Jakeman, John D.
作者单位	1.Sandia Natl Labs, Comp Sci Res Inst, 1450 Innovat Pkwy SE, Albuquerque, NM 87123 USA 2.Univ Utah, Sci Comp & Imaging SCI Inst, Salt Lake City, UT 84112 USA 3.Univ Utah, Math Dept, Salt Lake City, UT 84112 USA 4.Chinese Acad Sci, Inst Computat Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Jakeman, John D.,Narayan, Akil,Zhou, Tao. A GENERALIZED SAMPLING AND PRECONDITIONING SCHEME FOR SPARSE APPROXIMATION OF POLYNOMIAL CHAOS EXPANSIONS[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2017,39(3):A1114-A1144.
APA	Jakeman, John D.,Narayan, Akil,&Zhou, Tao.(2017).A GENERALIZED SAMPLING AND PRECONDITIONING SCHEME FOR SPARSE APPROXIMATION OF POLYNOMIAL CHAOS EXPANSIONS.SIAM JOURNAL ON SCIENTIFIC COMPUTING,39(3),A1114-A1144.
MLA	Jakeman, John D.,et al."A GENERALIZED SAMPLING AND PRECONDITIONING SCHEME FOR SPARSE APPROXIMATION OF POLYNOMIAL CHAOS EXPANSIONS".SIAM JOURNAL ON SCIENTIFIC COMPUTING 39.3(2017):A1114-A1144.