{"title":"低秩张量分解与逼近","authors":"Jiawang Nie, Li Wang, Zequn Zheng","doi":"10.1007/s40305-023-00455-7","DOIUrl":null,"url":null,"abstract":"Abstract There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.","PeriodicalId":44782,"journal":{"name":"Journal of the Operations Research Society of China","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Low Rank Tensor Decompositions and Approximations\",\"authors\":\"Jiawang Nie, Li Wang, Zequn Zheng\",\"doi\":\"10.1007/s40305-023-00455-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.\",\"PeriodicalId\":44782,\"journal\":{\"name\":\"Journal of the Operations Research Society of China\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Operations Research Society of China\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s40305-023-00455-7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Operations Research Society of China","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40305-023-00455-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
Abstract There exist linear relations among tensor entries of low rank tensors. These linear relations can be expressed by multi-linear polynomials, which are called generating polynomials. We use generating polynomials to compute tensor rank decompositions and low rank tensor approximations. We prove that this gives a quasi-optimal low rank tensor approximation if the given tensor is sufficiently close to a low rank one.
期刊介绍：
Journal of the Operations Research Society of China is the flagship journal of the Operations Research Society of China. Its primary goal is to promote researches and applications of all aspects of operational research. This journal provides a forum for practioners, academics and researchers in operational research and related fields. It will reflect the rapid social and economic development of China and lead to new problems and challenges which require new operations research methodology and techniques. It will publish 4 issues of one volume per year, including invited reviews, regular papers, short communications, book reviews and so on.
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