Constructing Least-Squares Polynomial Approximations

doi:10.1137/18M1234151

CSpace

	Constructing Least-Squares Polynomial Approximations
	Guo, Ling 1; Narayan, Akil 2,3; Zhou, Tao 4
	2020-06-01
发表期刊	SIAM REVIEW
ISSN	0036-1445
卷号	62 期号:2 页码:483-508
摘要	Polynomial approximations constructed using a least-squares approach form a ubiquitous technique in numerical computation. One of the simplest ways to generate data for least-squares problems is with random sampling of a function. We discuss theory and algorithms for stability of the least-squares problem using random samples. The main lesson from our discussion is that the intuitively straightforward ("standard") density for sampling frequently yields suboptimal approximations, whereas sampling from a non-standard density, called the induced distribution, yields near-optimal approximations. We present a recent, theory that demonstrates why sampling from the induced distribution is optimal and provide several numerical experiments that support the theory. Software is also provided that reproduces the figures in this paper.
关键词	least-squares approximations optimal sampling polynomial approximations
DOI	10.1137/18M1234151
收录类别	SCI
语种	英语
资助项目	NSF of China[11671265] ; NSF of China[11822111] ; NSF of China[11688101] ; NSF of China[91630312] ; NSF of China[91630203] ; NSF of China[11571351] ; NSF of China[11731006] ; AFOSR[FA9550-15-1-0467] ; NSF[DMS-1720416] ; Science Challenge Project[TZ2018001] ; National Key Basic Research Program[2018YFB0704304] ; Youth Innovation Promotion Association (CAS) ; NCMIS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000551389300006
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/51877
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, Ling
作者单位	1.Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China 2.Univ Utah, Dept Math, Salt Lake City, UT 84112 USA 3.Univ Utah, Sci Comp & Imaging SCI, Salt Lake City, UT 84112 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Guo, Ling,Narayan, Akil,Zhou, Tao. Constructing Least-Squares Polynomial Approximations[J]. SIAM REVIEW,2020,62(2):483-508.
APA	Guo, Ling,Narayan, Akil,&Zhou, Tao.(2020).Constructing Least-Squares Polynomial Approximations.SIAM REVIEW,62(2),483-508.
MLA	Guo, Ling,et al."Constructing Least-Squares Polynomial Approximations".SIAM REVIEW 62.2(2020):483-508.