0468385 20240103213306.120170105235959.9 85007372598 000394628800024 10.1016/j.cam.2016.12.007 Numerical CP Decomposition of Some Difficult Tensors 9 s. P cav_un_epca*02569330377-0427Journal of Computational and Applied Mathematics3171 (2017)362-370Elsevier Small matrix multiplication Canonical polyadic tensor decomposition Levenberg-Marquardt method cav_un_auth*0101212 Stochastická informatika Department of Stochastic Informatics SI SI Department of Stochastic Informatics 70 Tichavský Petr UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0274170 20 Phan A. H. JP cav_un_auth*0274171 10 Cichocki A. JP http://library.utia.cas.cz/separaty/2017/SI/tichavsky-0468385.pdf cav_un_auth*0303443 GA14-13713S GA ČR CZ 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, 3x3 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. BB 10000 10100 10102 2018 3 4 A hod 4ah 20231122142146.1 RVO:67985556 http://hdl.handle.net/11104/0270594 cav_un_auth*0303002 RIKEN JP 1 Department of Stochastic Informatics UTIA-B 20201 ENGINEERING, ELECTRICAL & ELECTRONIC S 1 Article Mathematics Applied 1 Article Mathematics Applied 1 Article Mathematics Applied MATHEMATICS.APPLIED 1.651 0.561 9.3 0.01943 0.684 12653 0.938 1.459 522 Q1 53.822 80.8 Q2 Q2 1.38 Q1 80.754 2017 Soubory v repozitáři: tichavsky-0468385.pdf 85007372598 SCOPUS PUBMED 000394628800024 WOS cav_un_epca*0256933 Journal of Computational and Applied Mathematics 0377-0427 1879-1778 Roč. 317 č. 1 2017 362 370 Elsevier