  The epsilon alternating least squares ($\epsilon$-ALS) is developed and
analyzed for canonical polyadic decomposition (approximation) of a higher-order
tensor where one or more of the factor matrices are assumed to be columnwisely
orthonormal. It is shown that the algorithm globally converges to a KKT point
for all tensors without any assumption. For the original ALS, by further
studying the properties of the polar decomposition, we also establish its
global convergence under a reality assumption not stronger than those in the
literature. These results completely address a question concerning the global
convergence raised in [L. Wang, M. T. Chu and B. Yu, \emph{SIAM J. Matrix Anal.
Appl.}, 36 (2015), pp. 1--19]. In addition, an initialization procedure is
proposed, which possesses a provable lower bound when the number of
columnwisely orthonormal factors is one. Armed with this initialization
procedure, numerical experiments show that the $\epsilon$-ALS exhibits a
promising performance in terms of efficiency and effectiveness.
