{"title":"Estimation of QTT Ranks of Regular Functions on a Uniform Square Grid","authors":"A. Zyl’, N. Zamarashkin","doi":"10.1134/s0965542524020143","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper proves estimates of <span>\\(\\varepsilon \\)</span>-ranks for TT decompositions of tensors obtained by tensorizing the values of a regular function of one complex variable on a uniform square grid in the complex plane. A relation between the approximation accuracy and the geometry of the domain of regularity of the function is established.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524020143","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
The paper proves estimates of \(\varepsilon \)-ranks for TT decompositions of tensors obtained by tensorizing the values of a regular function of one complex variable on a uniform square grid in the complex plane. A relation between the approximation accuracy and the geometry of the domain of regularity of the function is established.