| bibtype |
J -
Journal Article
|
| ARLID |
0468385 |
| utime |
20240103213306.1 |
| mtime |
20170105235959.9 |
| SCOPUS |
85007372598 |
| WOS |
000394628800024 |
| DOI |
10.1016/j.cam.2016.12.007 |
| title
(primary) (eng) |
Numerical CP Decomposition of Some Difficult Tensors |
| specification |
| page_count |
9 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0256933 |
| ISSN |
0377-0427 |
| title
|
Journal of Computational and Applied Mathematics |
| volume_id |
317 |
| volume |
1 (2017) |
| page_num |
362-370 |
| publisher |
|
|
| keyword |
Small matrix multiplication |
| keyword |
Canonical polyadic tensor decomposition |
| keyword |
Levenberg-Marquardt method |
| author
(primary) |
| ARLID |
cav_un_auth*0101212 |
| full_dept (cz) |
Stochastická informatika |
| full_dept (eng) |
Department of Stochastic Informatics |
| department (cz) |
SI |
| department (eng) |
SI |
| full_dept |
Department of Stochastic Informatics |
| share |
70 |
| name1 |
Tichavský |
| name2 |
Petr |
| institution |
UTIA-B |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| author
|
| ARLID |
cav_un_auth*0274170 |
| share |
20 |
| name1 |
Phan |
| name2 |
A. H. |
| country |
JP |
|
| author
|
| ARLID |
cav_un_auth*0274171 |
| share |
10 |
| name1 |
Cichocki |
| name2 |
A. |
| country |
JP |
|
| source |
|
| cas_special |
| project |
| ARLID |
cav_un_auth*0303443 |
| project_id |
GA14-13713S |
| agency |
GA ČR |
| country |
CZ |
|
| abstract
(eng) |
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. |
| RIV |
BB |
| FORD0 |
10000 |
| FORD1 |
10100 |
| FORD2 |
10102 |
| reportyear |
2018 |
| num_of_auth |
3 |
| mrcbC52 |
4 A hod 4ah 20231122142146.1 |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0270594 |
| cooperation |
| ARLID |
cav_un_auth*0303002 |
| name |
RIKEN |
| country |
JP |
|
| mrcbC64 |
1 Department of Stochastic Informatics UTIA-B 20201 ENGINEERING, ELECTRICAL & ELECTRONIC |
| confidential |
S |
| mrcbC86 |
1 Article Mathematics Applied |
| mrcbC86 |
1 Article Mathematics Applied |
| mrcbC86 |
1 Article Mathematics Applied |
| mrcbT16-e |
MATHEMATICSAPPLIED |
| mrcbT16-j |
0.684 |
| mrcbT16-s |
0.938 |
| mrcbT16-B |
53.822 |
| mrcbT16-D |
Q2 |
| mrcbT16-E |
Q2 |
| arlyear |
2017 |
| mrcbTft |
\nSoubory v repozitáři: tichavsky-0468385.pdf |
| mrcbU14 |
85007372598 SCOPUS |
| mrcbU24 |
PUBMED |
| mrcbU34 |
000394628800024 WOS |
| mrcbU63 |
cav_un_epca*0256933 Journal of Computational and Applied Mathematics 0377-0427 1879-1778 Roč. 317 č. 1 2017 362 370 Elsevier |
|