Name
Abstract | ||
|---|---|---|
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 LevenbergMarquardt optimization. Numerical results indicate the rank and border ranks of tensors that correspond to multiplication of matrices of the size 23 and 32, 33 and 32, 33 and 33, and 34 and 43. The ranks are 11, 15, 23 and 29, respectively. In particular, a novel algorithm for computing product of matrices of the sizes 34 and 43 using 29 multiplications is presented. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.cam.2016.12.007 | J. Computational Applied Mathematics |
Keywords | DocType | Volume |
Small matrix multiplication,Canonical polyadic tensor decomposition,Levenberg–Marquardt method | Journal | abs/1603.01372 |
Issue | ISSN | Citations |
C | 0377-0427 | 3 |
PageRank | References | Authors |
0.40 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Petr Tichavský | 1 | 341 | 41.01 |
| Anh Huy Phan | 2 | 828 | 51.60 |
| Andrzej Cichocki | 3 | 5228 | 508.42 |