Shared-memory parallelization of MTTKRP for dense tensors

The matricized-tensor times Khatri-Rao product (MTTKRP) is the computational bottleneck for algorithms computing CP decompositions of tensors. In this work, we develop shared-memory parallel algorithms for MTTKRP involving dense tensors. The algorithms cast nearly all of the computation as matrix operations in order to use optimized BLAS subroutines, and they avoid reordering tensor entries in memory. We use our parallel implementation to compute a CP decomposition of a neuroimaging data set and achieve a speedup of up to 7.4X over existing parallel software.