Nonlinear Least Squares Solver for Evaluating Canonical Tensor Decomposition

摘要

Nonlinear least squares iterative solver developed earlier by the author is applied for numerical solution of special system of multilinear equations arising in the problem of canonical tensor decomposition. The proposed algorithm is based on easily parallelizable computational kernels such as matrix-vector multiplications and elementary vector operations and therefore has a potential for a quite efficient implementation on modern high-performance computers. The results of numerical testing presented for certain examples of large scale dense and medium size sparse 3D tensors found in existing literature seem very competitive with respect to computational costs involved.