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Maximum relative distance between real rank-two and rank-one tensors

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Bibliographic Details
Main Authors: Henrik, Eisenmann, André, Uschmajew
Format: Book
Language:English
Published: Springer 2023
Subjects:
Frobenius norm
rank-one approximation
Online Access:https://link.springer.com/article/10.1007/s10231-022-01268-w
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7449
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spelling oai:localhost:PNK-74492023-04-03T08:41:37Z Maximum relative distance between real rank-two and rank-one tensors Henrik, Eisenmann André, Uschmajew Frobenius norm rank-one approximation CC BY It is shown that the relative distance in Frobenius norm of a real symmetric order-d tensor of rank-two to its best rank-one approximation is upper bounded by 1−(1−1/d)d−1−−−−−−−−−−−−−√. This is achieved by determining the minimal possible ratio between spectral and Frobenius norm for symmetric tensors of border rank two, which equals (1−1/d)(d−1)/2. These bounds are also verified for arbitrary real rank-two tensors by reducing to the symmetric case. 2023-04-03T08:41:37Z 2023-04-03T08:41:37Z 2022 Book https://link.springer.com/article/10.1007/s10231-022-01268-w https://dlib.phenikaa-uni.edu.vn/handle/PNK/7449 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic Frobenius norm
rank-one approximation
spellingShingle Frobenius norm
rank-one approximation
Henrik, Eisenmann
André, Uschmajew
Maximum relative distance between real rank-two and rank-one tensors
description CC BY
format Book
author Henrik, Eisenmann
André, Uschmajew
author_facet Henrik, Eisenmann
André, Uschmajew
author_sort Henrik, Eisenmann
title Maximum relative distance between real rank-two and rank-one tensors
title_short Maximum relative distance between real rank-two and rank-one tensors
title_full Maximum relative distance between real rank-two and rank-one tensors
title_fullStr Maximum relative distance between real rank-two and rank-one tensors
title_full_unstemmed Maximum relative distance between real rank-two and rank-one tensors
title_sort maximum relative distance between real rank-two and rank-one tensors
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s10231-022-01268-w
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7449
_version_ 1762184304840933376
score 8.893527

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