Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable

We prove the existence of an open set of n1 ×n2 ×n3 tensors of rank r for which popular and e?cient algorithms for computing tensor rank decompositions based on a reduction to a linear matrix pencil, typically followed by a generalized eigendecomposition, are arbitrarily numerically forward unstable...

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Detalles Bibliográficos
Autores: Beltrán Álvarez, Carlos|||0000-0002-0689-8232, Breiding, Paul, Vannieuwenhoven, Nick
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/18159
Acceso en línea:http://hdl.handle.net/10902/18159
Access Level:acceso abierto
Palabra clave:Jennrich’s algorithm
Canonical polyadic decomposition
Tensor rank decomposition
Numerical instability
CPD
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spelling Pencil-Based Algorithms For Tensor Rank Decomposition Are Not StableBeltrán Álvarez, Carlos|||0000-0002-0689-8232Breiding, PaulVannieuwenhoven, NickJennrich’s algorithmCanonical polyadic decompositionTensor rank decompositionNumerical instabilityCPDWe prove the existence of an open set of n1 ×n2 ×n3 tensors of rank r for which popular and e?cient algorithms for computing tensor rank decompositions based on a reduction to a linear matrix pencil, typically followed by a generalized eigendecomposition, are arbitrarily numerically forward unstable. Our analysis shows that this problem is caused by the fact that the condition number of tensor rank decomposition can be much larger for n1 ×n2 ×2 tensors than for the n1 ×n2 ×n3 input tensor. Moreover, we present a lower bound for the limiting distribution of the condition number of random tensor rank decompositions of third-order tensors. The numerical experiments illustrate that for random tensor rank decompositions one should anticipate a loss of precision of a few digits.Society for Industrial and Applied MathematicsUniversidad de Cantabria20192019-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/18159SIAM J. MATRIX ANAL. APPL.Vol. 40, No. 2, pp. 739–773reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/181592026-06-02T12:39:31Z
dc.title.none.fl_str_mv Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
title Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
spellingShingle Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
Beltrán Álvarez, Carlos|||0000-0002-0689-8232
Jennrich’s algorithm
Canonical polyadic decomposition
Tensor rank decomposition
Numerical instability
CPD
title_short Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
title_full Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
title_fullStr Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
title_full_unstemmed Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
title_sort Pencil-Based Algorithms For Tensor Rank Decomposition Are Not Stable
dc.creator.none.fl_str_mv Beltrán Álvarez, Carlos|||0000-0002-0689-8232
Breiding, Paul
Vannieuwenhoven, Nick
author Beltrán Álvarez, Carlos|||0000-0002-0689-8232
author_facet Beltrán Álvarez, Carlos|||0000-0002-0689-8232
Breiding, Paul
Vannieuwenhoven, Nick
author_role author
author2 Breiding, Paul
Vannieuwenhoven, Nick
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Jennrich’s algorithm
Canonical polyadic decomposition
Tensor rank decomposition
Numerical instability
CPD
topic Jennrich’s algorithm
Canonical polyadic decomposition
Tensor rank decomposition
Numerical instability
CPD
description We prove the existence of an open set of n1 ×n2 ×n3 tensors of rank r for which popular and e?cient algorithms for computing tensor rank decompositions based on a reduction to a linear matrix pencil, typically followed by a generalized eigendecomposition, are arbitrarily numerically forward unstable. Our analysis shows that this problem is caused by the fact that the condition number of tensor rank decomposition can be much larger for n1 ×n2 ×2 tensors than for the n1 ×n2 ×n3 input tensor. Moreover, we present a lower bound for the limiting distribution of the condition number of random tensor rank decompositions of third-order tensors. The numerical experiments illustrate that for random tensor rank decompositions one should anticipate a loss of precision of a few digits.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/18159
url http://hdl.handle.net/10902/18159
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv SIAM J. MATRIX ANAL. APPL.Vol. 40, No. 2, pp. 739–773
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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