A new convergence proof for the higher-order power method and generalizations
This work addresses a theoretical gap in tensor decomposition for researchers in numerical linear algebra and optimization, but the result is incremental as it applies existing theory to a known algorithm.
The paper provides a convergence proof for the higher-order power method for tensors, showing that the factors converge point-wise to a critical point by applying Łojasiewicz inequalities to the equivalent alternating least squares algorithm.
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 Łojasiewicz inequalities to the equivalent, unconstrained alternating least squares algorithm for best rank-one tensor approximation.