An adaptive algebraic multigrid algorithm for low-rank canonical tensor decomposition

Abstract: This paper presents a multigrid algorithm for the computation of the rank-R canonical decomposition of a tensor for low rank R. Standard alternating least squares (ALS) is used as the relaxation method. Transfer operators and coarse-level tensors are constructed in an adaptive setup phase based on multiplicative correction and on Bootstrap algebraic multigrid. An accurate solution is then computed by an additive solve phase based on the Full Approximation Scheme. Numerical tests show that for certain test problems the multilevel method significantly outperforms standalone ALS when a high level of accuracy is required.