  We study the convergence of the Regularized Alternating Least-Squares
algorithm for tensor decompositions. As a main result, we have shown that given
the existence of critical points of the Alternating Least-Squares method, the
limit points of the converging subsequences of the RALS are the critical points
of the least squares cost functional. Some numerical examples indicate a faster
convergence rate for the RALS in comparison to the usual alternating least
squares method.
