A CHRISTOFFEL FUNCTION WEIGHTED LEAST SQUARES ALGORITHM FOR COLLOCATION APPROXIMATIONS

doi:10.1090/mcom/3192

	A CHRISTOFFEL FUNCTION WEIGHTED LEAST SQUARES ALGORITHM FOR COLLOCATION APPROXIMATIONS
	Narayan, Akil 1,2; Jakeman, John D.3; Zhou, Tao4
	2017-07-01
发表期刊	MATHEMATICS OF COMPUTATION
ISSN	0025-5718
卷号	86 期号:306 页码:1913-1947
摘要	We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation framework. Our investigation is motivated by applications in the collocation approximation of parametric functions, which frequently entails construction of surrogates via orthogonal polynomials. A standard Monte Carlo approach would draw samples according to the density defining the orthogonal polynomial family. Our proposed algorithm instead samples with respect to the ( weighted) pluripotential equilibrium measure of the domain, and subsequently solves a weighted least-squares problem, with weights given by evaluations of the Christoffel function. 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.
DOI	10.1090/mcom/3192
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]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000398823400017
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25291
专题	计算数学与科学工程计算研究所
通讯作者	Narayan, Akil
作者单位	1.Univ Utah, Dept Math, Salt Lake City, UT 84112 USA 2.Univ Utah, SCI Inst, Salt Lake City, UT 84112 USA 3.Sandia Natl Labs, Comp Sci Res Inst, 1450 Innovat Pkwy SE, Albuquerque, NM 87123 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Narayan, Akil,Jakeman, John D.,Zhou, Tao. A CHRISTOFFEL FUNCTION WEIGHTED LEAST SQUARES ALGORITHM FOR COLLOCATION APPROXIMATIONS[J]. MATHEMATICS OF COMPUTATION,2017,86(306):1913-1947.
APA	Narayan, Akil,Jakeman, John D.,&Zhou, Tao.(2017).A CHRISTOFFEL FUNCTION WEIGHTED LEAST SQUARES ALGORITHM FOR COLLOCATION APPROXIMATIONS.MATHEMATICS OF COMPUTATION,86(306),1913-1947.
MLA	Narayan, Akil,et al."A CHRISTOFFEL FUNCTION WEIGHTED LEAST SQUARES ALGORITHM FOR COLLOCATION APPROXIMATIONS".MATHEMATICS OF COMPUTATION 86.306(2017):1913-1947.