Numerical CP Decomposition of Some Difficult Tensors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00468385" target="_blank" >RIV/67985556:_____/17:00468385 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.cam.2016.12.007" target="_blank" >http://dx.doi.org/10.1016/j.cam.2016.12.007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2016.12.007" target="_blank" >10.1016/j.cam.2016.12.007</a>

Result language
angličtina
Original language name
Numerical CP Decomposition of Some Difficult Tensors
Original language description
In this paper, a numerical method is proposed for canonical polyadic (CP) decomposition of small size tensors. The focus is primarily on decomposition of tensors that correspond to small matrix multiplications. Here, rank of the tensors is equal to the smallest number of scalar multiplications that are necessary to accomplish the matrix multiplication. The proposed method is based on a constrained Levenberg-Marquardt optimization. Numerical results indicate the rank and border ranks of tensors that correspond to multiplication of matrices of the size 2x3 and 3x2, 3x3 and 3x2,n3x3 and 3x3, and 3x4 and 4x3. The ranks are 11, 15, 23 and 29, respectively. In particular, a novel algorithm for computing product of matrices of the sizes 3x4 and 4x3 using 29 multiplications is presented.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA14-13713S" target="_blank" >GA14-13713S: Tensor Decomposition Methods and Their Applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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