A new convergence proof for the higher-order power method and   generalizations
  A proof for the point-wise convergence of the factors in the higher-order power method for tensors towards a critical point is given. It is obtained by applying established results from the theory of \L{}ojasiewicz inequalities to the equivalent, unconstrained alternating least squares algorithm for best rank-one tensor approximation. 
Andr\'e Uschmajew
math.OC math.NA