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 |
| DOI | 10.1090/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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