On best rank one approximation of tensors
For researchers working on tensor decompositions, this provides a more reliable algorithm for rank-one approximation, though it is an incremental improvement over existing methods.
The paper proposes a new algorithm, alternating singular value decomposition, for computing the best rank-one approximation of tensors, with a modification to ensure convergence to a semi-maximal point. Numerical examples show improved computational performance over the alternating least squares method.
In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating iterations will always converge to a semi-maximal point. (A critical point in several vector variables is semi-maximal if it is maximal with respect to each vector variable, while other vector variables are kept fixed.) We present several numerical examples that illustrate the computational performance of the new method in comparison to the alternating least square method.