  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 multiplying the matrices of the sizes 3x3 and 3x2 with 15 multiplications
is presented.
