Isabella Furci, Andrea Adriani, Stefano Serra-Capizzano
{"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}
引用次数: 0
Abstract
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.