SYMMETRIC TENSOR DECOMPOSITION BY AN ITERATIVE EIGENDECOMPOSITION ALGORITHM

Abstract. We present an iterative algorithm, called the symmetric tensor eigen-rank-one itera-tive decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination of symmetric rank-1 unit-norm outer factors using only eigendecompositions and least-squares fit-ting. Originally designed for a symmetric tensor with an order being a power of two, STEROID is shown to be applicable to any order through an innovative tensor embedding technique. Numerical examples demonstrate the high efficiency and accuracy of the proposed scheme even for large scale problems. Key words. Symmetric tensor, decomposition, rank-1, eigendecomposition, least-squares AMS subject classifications. 15A69,15A18,15A2