{"title":"Convergence properties of sequences related to the Ando–Li–Mathias construction and to the weighted Cheap mean","authors":"Dario A. Bini, Bruno Iannazzo, Jie Meng","doi":"10.1007/s43036-024-00411-z","DOIUrl":null,"url":null,"abstract":"<div><p>Sequences defining a weighted matrix geometric mean are investigated and their convergence speed is analyzed. The superlinear convergence of a weighted mean based on the Ando–Li–Mathias (ALM) construction is proved. A weighted Cheap mean is defined and conditions on the weights for linear or superlinear convergence of order at least three are provided.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00411-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Sequences defining a weighted matrix geometric mean are investigated and their convergence speed is analyzed. The superlinear convergence of a weighted mean based on the Ando–Li–Mathias (ALM) construction is proved. A weighted Cheap mean is defined and conditions on the weights for linear or superlinear convergence of order at least three are provided.
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