Low Rank Tensor Decompositions and Approximations

IF 0.9 4区数学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Journal of the Operations Research Society of China Pub Date : 2023-03-18 DOI:10.1007/s40305-023-00455-7

Jiawang Nie, Li Wang, Zequn Zheng

引用次数: 0

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.

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低秩张量分解与逼近

摘要低秩张量张量项之间存在线性关系。这些线性关系可以用多线性多项式表示，称为生成多项式。我们使用生成多项式来计算张量秩分解和低秩张量近似。我们证明了如果给定张量足够接近低秩张量，则给出了准最优低秩张量近似。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the Operations Research Society of China OPERATIONS RESEARCH & MANAGEMENT SCIENCE-

CiteScore

3.30

自引率

0.00%

发文量

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.