Approximate Real Symmetric Tensor Rank

被引：0

作者：

Ergür A.A. ^{[1
]}

Rebollo Bueno J. ^{[3
]}

Valettas P. ^{[2
]}

机构：

[1] Mathematics and Computer Science, The University of Texas at San Antonio, San Antonio, TX

[2] Mathematics & Electrical Enginering and Computer Science, University of Missouri, Columbia, MO

[3] Mathematics, The University of Texas at San Antonio, San Antonio, TX

来源：

Arnold Mathematical Journal | 2023年 / 9卷 / 4期

关键词：

Approximate Sparsification; Energy Increment Method; Maurey’s Empricial Method; Polynomial Optimization; Symmetric Tensor Rank;

D O I：

10.1007/s40598-023-00235-4

中图分类号：

学科分类号：

摘要：

We investigate the effect of an ε -room of perturbation tolerance on symmetric tensor decomposition. To be more precise, suppose a real symmetric d-tensor f, a norm ∥ · ∥ on the space of symmetric d-tensors, and ε> 0 are given. What is the smallest symmetric tensor rank in the ε -neighborhood of f? In other words, what is the symmetric tensor rank of f after a clever ε -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. © 2023, Institute for Mathematical Sciences (IMS), Stony Brook University, NY.

引用

页码：455 / 480

页数：25

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