Algorithms for Structure Preserving Best Rank-one Approximations of Partially Symmetric Tensors

Abstract

Based on the alternating least squares (ALS) technique and the singular value decomposition (SVD) technique, the algorithms for finding the structure preserving best rank-one approximations of even order paired symmetric tensors and k-mode symmetric tensors are presented. Then the convergence of the algorithms is discussed. Some numerical examples and applications are given to illustrate the feasibility and effectiveness of the proposed algorithms.