正半定锥交替投影序列的解析公式及其在收敛分析中的应用

IF 1.2 3区 数学 Q1 MATHEMATICS
Hiroyuki Ochiai , Yoshiyuki Sekiguchi , Hayato Waki
{"title":"正半定锥交替投影序列的解析公式及其在收敛分析中的应用","authors":"Hiroyuki Ochiai ,&nbsp;Yoshiyuki Sekiguchi ,&nbsp;Hayato Waki","doi":"10.1016/j.jmaa.2024.129070","DOIUrl":null,"url":null,"abstract":"<div><div>We derive analytic formulas for the alternating projection method applied to the cone <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the upper bound given by the singularity degree is actually tight when the alternating projection method is applied to <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> and a 3-plane whose intersection is a singleton with singularity degree 2.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 1","pages":"Article 129070"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analytic formulas for alternating projection sequences for the positive semidefinite cone and an application to convergence analysis\",\"authors\":\"Hiroyuki Ochiai ,&nbsp;Yoshiyuki Sekiguchi ,&nbsp;Hayato Waki\",\"doi\":\"10.1016/j.jmaa.2024.129070\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We derive analytic formulas for the alternating projection method applied to the cone <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the upper bound given by the singularity degree is actually tight when the alternating projection method is applied to <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mo>+</mo></mrow><mrow><mn>3</mn></mrow></msubsup></math></span> and a 3-plane whose intersection is a singleton with singularity degree 2.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"544 1\",\"pages\":\"Article 129070\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-11-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24009922\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009922","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

我们推导出交替投影法的解析公式,该方法适用于正半有限矩阵的锥 S+n 和仿射子空间。更准确地说,我们找到了代表交替投影法所构建序列的参数的递推关系。通过应用这些公式,我们详细分析了交替投影法,并证明当交替投影法应用于 S+3 和一个交点为奇异度为 2 的单子的 3 平面时,奇异度给出的上界实际上是紧密的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analytic formulas for alternating projection sequences for the positive semidefinite cone and an application to convergence analysis
We derive analytic formulas for the alternating projection method applied to the cone S+n of positive semidefinite matrices and an affine subspace. More precisely, we find recursive relations on parameters representing a sequence constructed by the alternating projection method. By applying these formulas, we analyze the alternating projection method in detail and show that the upper bound given by the singularity degree is actually tight when the alternating projection method is applied to S+3 and a 3-plane whose intersection is a singleton with singularity degree 2.
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
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信