中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
A CHRISTOFFEL FUNCTION WEIGHTED LEAST SQUARES ALGORITHM FOR COLLOCATION APPROXIMATIONS

文献类型:期刊论文

作者Narayan, Akil1,2; Jakeman, John D.3; Zhou, Tao4
刊名MATHEMATICS OF COMPUTATION
出版日期2017-07-01
卷号86期号:306页码:1913-1947
ISSN号0025-5718
DOI10.1090/mcom/3192
英文摘要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.
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
语种英语
WOS记录号WOS:000398823400017
出版者AMER MATHEMATICAL SOC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/25290]  
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.

入库方式: OAI收割

来源:数学与系统科学研究院

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