块结构矩阵序列及其频谱和奇异值规范分布:一般理论

Isabella Furci, Andrea Adriani, Stefano Serra-Capizzano
{"title":"块结构矩阵序列及其频谱和奇异值规范分布:一般理论","authors":"Isabella Furci, Andrea Adriani, Stefano Serra-Capizzano","doi":"arxiv-2409.06465","DOIUrl":null,"url":null,"abstract":"In recent years more and more involved block structures appeared in the\nliterature in the context of numerical approximations of complex infinite\ndimensional operators modeling real-world applications. In various settings,\nthanks the theory of generalized locally Toeplitz matrix-sequences, the\nasymptotic distributional analysis is well understood, but a general theory is\nmissing when general block structures are involved. The central part of the\ncurrent work deals with such a delicate generalization when blocks are of\n(block) unilevel Toeplitz type, starting from a problem of recovery with\nmissing data. Visualizations, numerical tests, and few open problems are\npresented and critically discussed.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Block structured matrix-sequences and their spectral and singular value canonical distributions: a general theory\",\"authors\":\"Isabella Furci, Andrea Adriani, Stefano Serra-Capizzano\",\"doi\":\"arxiv-2409.06465\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In recent years more and more involved block structures appeared in the\\nliterature in the context of numerical approximations of complex infinite\\ndimensional operators modeling real-world applications. In various settings,\\nthanks the theory of generalized locally Toeplitz matrix-sequences, the\\nasymptotic distributional analysis is well understood, but a general theory is\\nmissing when general block structures are involved. The central part of the\\ncurrent work deals with such a delicate generalization when blocks are of\\n(block) unilevel Toeplitz type, starting from a problem of recovery with\\nmissing data. Visualizations, numerical tests, and few open problems are\\npresented and critically discussed.\",\"PeriodicalId\":501162,\"journal\":{\"name\":\"arXiv - MATH - Numerical Analysis\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06465\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06465","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

近年来,在对现实世界应用中的复杂无穷维算子进行数值逼近建模的背景下,越来越多的块状结构出现在文献中。得益于广义局部托普利兹矩阵序列理论,在各种情况下的渐近分布分析都得到了很好的理解,但在涉及一般块状结构时,却缺少一个通用理论。当前工作的核心部分就是从丢失数据的恢复问题入手,研究当块是单级托普利茨类型时,如何进行这种微妙的概括。本文介绍了可视化、数值测试和一些未决问题,并对其进行了批判性讨论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Block structured matrix-sequences and their spectral and singular value canonical distributions: a general theory
In recent years more and more involved block structures appeared in the literature in the context of numerical approximations of complex infinite dimensional operators modeling real-world applications. In various settings, thanks the theory of generalized locally Toeplitz matrix-sequences, the asymptotic distributional analysis is well understood, but a general theory is missing when general block structures are involved. The central part of the current work deals with such a delicate generalization when blocks are of (block) unilevel Toeplitz type, starting from a problem of recovery with missing data. Visualizations, numerical tests, and few open problems are presented and critically discussed.
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
自引率
0.00%
发文量
0
×
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