In this paper, we discuss the acceleration of the regularized alternating
least square (RALS) algorithm for tensor approximation. We propose a fast
iterative method using a Aitken-Stefensen like updates for the regularized
algorithm. Through numerical experiments, the fast algorithm demonstrate a
faster convergence rate for the accelerated version in comparison to both the
standard and regularized alternating least squares algorithms. In addition, we
analyze the global convergence based on the Kurdyka- Lojasiewicz inequality as
well as show that the RALS algorithm has a linear local convergence rate.