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The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite

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Main Authors: Carlos, Beltrán, Paul, Breiding, Nick, Vannieuwenhoven
Format: Book
Language:English
Published: Springer 2023
Subjects:
sum of rank-1 tensors
structured perturbations
Online Access:https://dlib.phenikaa-uni.edu.vn/handle/PNK/7446
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spelling oai:localhost:PNK-74462023-04-03T08:10:18Z The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite Carlos, Beltrán Paul, Breiding Nick, Vannieuwenhoven sum of rank-1 tensors structured perturbations CC BY The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with respect to structured perturbations. Those are perturbations preserving the rank of the tensor that is decomposed. On the other hand, the angular condition number measures the perturbations of the rank-1 summands up to scaling. We show for random rank-2 tensors that the expected value of the condition number is infinite for a wide range of choices of the density. 2023-04-03T08:10:18Z 2023-04-03T08:10:18Z 2022 Book https://dlib.phenikaa-uni.edu.vn/handle/PNK/7446 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic sum of rank-1 tensors
structured perturbations
spellingShingle sum of rank-1 tensors
structured perturbations
Carlos, Beltrán
Paul, Breiding
Nick, Vannieuwenhoven
The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
description CC BY
format Book
author Carlos, Beltrán
Paul, Breiding
Nick, Vannieuwenhoven
author_facet Carlos, Beltrán
Paul, Breiding
Nick, Vannieuwenhoven
author_sort Carlos, Beltrán
title The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
title_short The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
title_full The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
title_fullStr The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
title_full_unstemmed The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
title_sort average condition number of most tensor rank decomposition problems is infinite
publisher Springer
publishDate 2023
url https://dlib.phenikaa-uni.edu.vn/handle/PNK/7446
_version_ 1762184304565157888
score 8.891053

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