Constructing Least-Squares Polynomial Approximations
文献类型：期刊论文
| 作者 | Guo, Ling2; Narayan, Akil1,3; Zhou, Tao4 |
| 刊名 | SIAM REVIEW
 |
| 出版日期 | 2020-06-01 |
| 卷号 | 62期号:2页码:483-508 |
| 关键词 | least-squares approximations optimal sampling polynomial approximations |
| ISSN号 | 0036-1445 |
| DOI | 10.1137/18M1234151 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000551389300006 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51876]  |
| 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.Univ Utah, Sci Comp & Imaging SCI, Salt Lake City, UT 84112 USA 2.Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China 3.Univ Utah, Dept Math, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。