Approximate Real Symmetric Tensor Rank
Approximate Real Symmetric Tensor Rank
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近似实对称张量秩
DOI：
10.1007/s40598-023-00235-4
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发表时间：
2023
影响因子：
--
通讯作者：
Valettas, Petros
中科院分区：
文献类型：
--
作者：
Ergür, Alperen A.;Rebollo Bueno, Jesus;Valettas, Petros
We investigate the effect of an-room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetricd-tensorf, a norm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\Vert \cdot \right\Vert $$\end{document} on the space of symmetricd-tensors, andare given. What is the smallest symmetric tensor rank in the-neighborhood off? In other words, what is the symmetric tensor rank offafter a clever-perturbation? We prove two theorems and develop three corresponding algorithms that give constructive upper bounds for this question. With expository goals in mind, we present probabilistic and convex geometric ideas behind our results, reproduce some known results, and point out open problems.
We investigate the effect of an-room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetricd-tensorf, a norm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\Vert \cdot \right\Vert $$\end{document} on the space of symmetricd-tensors, andare given. What is the smallest symmetric tensor rank in the-neighborhood off? In other words, what is the symmetric tensor rank offafter a clever-perturbation? We prove two theorems and develop three corresponding algorithms that give constructive upper bounds for this question. With expository goals in mind, we present probabilistic and convex geometric ideas behind our results, reproduce some known results, and point out open problems.
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