Matches in SemOpenAlex for { <https://semopenalex.org/work/W588102005> ?p ?o ?g. }
Showing items 1 to 90 of
90
with 100 items per page.
- W588102005 endingPage "792" @default.
- W588102005 startingPage "775" @default.
- W588102005 abstract "The uniqueness of the best rank-one approximation of a tensor under the Frobenius norm is a basic and important studying subject in the tensor theory. By introducing the quasi-singular value of a tensor, we present a new sufficient condition under which the best rank-one approximation of a nonzero tensor $underline{X}inmathbb{R}^{d_{1}times d_{2}times d_{3}}$ is unique and obtain that the set consisting of all tensors satisfying the sufficient condition is an open and dense set in $mathbb{R}^{d_{1}times d_{2}times d_{3}}$. In addition, we present a necessary and sufficient condition under which the best rank-one approximation of the sum tensor $underline{tilde X}=underline{X} + {underline E}$ under some assumption on the tensor $underline{tilde X}inmathbb{R}^{d_{1}times d_{2}times d_{3}}$ is equal to the best rank-one approximation of ${underline X}$. Meanwhile, a numerical algorithm is proposed for computing the quasi-singular value of a tensor. Finally, several testing examples are presented to illustrate the feasibility of the computational process and the correctness of the theoretical results obtained in the paper." @default.
- W588102005 created "2016-06-24" @default.
- W588102005 creator A5034372090 @default.
- W588102005 creator A5076533682 @default.
- W588102005 date "2015-01-01" @default.
- W588102005 modified "2023-09-25" @default.
- W588102005 title "On the Uniqueness and Perturbation to the Best Rank-One Approximation of a Tensor" @default.
- W588102005 cites W1986680416 @default.
- W588102005 cites W1986782029 @default.
- W588102005 cites W1992426838 @default.
- W588102005 cites W2002598080 @default.
- W588102005 cites W2004026774 @default.
- W588102005 cites W2010988913 @default.
- W588102005 cites W2013912476 @default.
- W588102005 cites W2018282388 @default.
- W588102005 cites W2019819801 @default.
- W588102005 cites W2024165284 @default.
- W588102005 cites W2060225944 @default.
- W588102005 cites W2066392792 @default.
- W588102005 cites W2070013413 @default.
- W588102005 cites W2114613785 @default.
- W588102005 cites W2132267493 @default.
- W588102005 cites W2167602604 @default.
- W588102005 cites W2569661359 @default.
- W588102005 cites W3102183770 @default.
- W588102005 doi "https://doi.org/10.1137/140975577" @default.
- W588102005 hasPublicationYear "2015" @default.
- W588102005 type Work @default.
- W588102005 sameAs 588102005 @default.
- W588102005 citedByCount "11" @default.
- W588102005 countsByYear W5881020052017 @default.
- W588102005 countsByYear W5881020052018 @default.
- W588102005 countsByYear W5881020052019 @default.
- W588102005 countsByYear W5881020052020 @default.
- W588102005 countsByYear W5881020052021 @default.
- W588102005 countsByYear W5881020052023 @default.
- W588102005 crossrefType "journal-article" @default.
- W588102005 hasAuthorship W588102005A5034372090 @default.
- W588102005 hasAuthorship W588102005A5076533682 @default.
- W588102005 hasConcept C11413529 @default.
- W588102005 hasConcept C114614502 @default.
- W588102005 hasConcept C121332964 @default.
- W588102005 hasConcept C134306372 @default.
- W588102005 hasConcept C155281189 @default.
- W588102005 hasConcept C158693339 @default.
- W588102005 hasConcept C164226766 @default.
- W588102005 hasConcept C20178491 @default.
- W588102005 hasConcept C202444582 @default.
- W588102005 hasConcept C2777021972 @default.
- W588102005 hasConcept C33923547 @default.
- W588102005 hasConcept C520416788 @default.
- W588102005 hasConcept C55439883 @default.
- W588102005 hasConcept C62520636 @default.
- W588102005 hasConcept C92207270 @default.
- W588102005 hasConceptScore W588102005C11413529 @default.
- W588102005 hasConceptScore W588102005C114614502 @default.
- W588102005 hasConceptScore W588102005C121332964 @default.
- W588102005 hasConceptScore W588102005C134306372 @default.
- W588102005 hasConceptScore W588102005C155281189 @default.
- W588102005 hasConceptScore W588102005C158693339 @default.
- W588102005 hasConceptScore W588102005C164226766 @default.
- W588102005 hasConceptScore W588102005C20178491 @default.
- W588102005 hasConceptScore W588102005C202444582 @default.
- W588102005 hasConceptScore W588102005C2777021972 @default.
- W588102005 hasConceptScore W588102005C33923547 @default.
- W588102005 hasConceptScore W588102005C520416788 @default.
- W588102005 hasConceptScore W588102005C55439883 @default.
- W588102005 hasConceptScore W588102005C62520636 @default.
- W588102005 hasConceptScore W588102005C92207270 @default.
- W588102005 hasIssue "2" @default.
- W588102005 hasLocation W5881020051 @default.
- W588102005 hasOpenAccess W588102005 @default.
- W588102005 hasPrimaryLocation W5881020051 @default.
- W588102005 hasRelatedWork W1963699590 @default.
- W588102005 hasRelatedWork W2069287942 @default.
- W588102005 hasRelatedWork W2153806284 @default.
- W588102005 hasRelatedWork W2767478428 @default.
- W588102005 hasRelatedWork W2902280532 @default.
- W588102005 hasRelatedWork W2980991378 @default.
- W588102005 hasRelatedWork W2982211507 @default.
- W588102005 hasRelatedWork W3168529202 @default.
- W588102005 hasRelatedWork W4213309379 @default.
- W588102005 hasRelatedWork W4296020528 @default.
- W588102005 hasVolume "36" @default.
- W588102005 isParatext "false" @default.
- W588102005 isRetracted "false" @default.
- W588102005 magId "588102005" @default.
- W588102005 workType "article" @default.