{"title":"估计均匀正方形网格上正则函数的 QTT 等级","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":"{\"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}","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}
Estimation of QTT Ranks of Regular Functions on a Uniform Square Grid
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.