最接近旋转矩阵问题的求解方法:比较综述

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-21 DOI:10.1002/nla.2492

Soheil Sarabandi, Federico Thomas

{"title":"最接近旋转矩阵问题的求解方法:比较综述","authors":"Soheil Sarabandi, Federico Thomas","doi":"10.1002/nla.2492","DOIUrl":null,"url":null,"abstract":"Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed‐form methods are as robust as the SVD, but significantly faster and more accurate.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Solution methods to the nearest rotation matrix problem in ℝ3 : A comparative survey\",\"authors\":\"Soheil Sarabandi, Federico Thomas\",\"doi\":\"10.1002/nla.2492\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed‐form methods are as robust as the SVD, but significantly faster and more accurate.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1002/nla.2492\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/nla.2492","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 1

摘要

目前，奇异值分解(SVD)是求解最近旋转矩阵问题的标准方法。然而，许多其他的方法是可用的在三维情况下的文献。本文综述了最具代表性的几种方法，提出了几种替代方法，并进行了比较分析，以阐明它们的相对计算成本和误差性能。这一分析得出的结论是，一些代数闭形方法与奇异值分解一样鲁棒，但速度更快，更准确。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Solution methods to the nearest rotation matrix problem in ℝ3 : A comparative survey

Nowadays, the singular value decomposition (SVD) is the standard method of choice for solving the nearest rotation matrix problem. Nevertheless, many other methods are available in the literature for the 3D case. This article reviews the most representative ones, proposes alternative ones, and presents a comparative analysis to elucidate their relative computational costs and error performances. This analysis leads to the conclusion that some algebraic closed‐form methods are as robust as the SVD, but significantly faster and more accurate.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.