A modified Newton’s method for best rank-one approximation to tensors

In this paper, a modified Newton’s method for the best rank-one approximation problem to tensor is proposed. We combine the iterative matrix of Jacobi–Gauss–Newton (JGN) algorithm or Alternating Least Squares (ALS) algorithm with the iterative matrix of GRQ-Newton method, and present a modified version of GRQ-Newton algorithm. A line search along the projective direction is employed to obtain the global convergence. Preliminary numerical experiments and numerical comparison show that our algorithm is efficient.