On abelian tensor decomposition and gradient-descent algorithm

Abstract

Volker Strassen introduced a famous commutation equation on tensor rank in his ground-breaking papers [9, 10]. Abelian tensor are rank-I tensors in K I×I×K satisfying Strassen’s equation. In this paper, we introduce Abelian tensor decomposition, which is unique under mild conditions. A gradient based algorithm has been given and the optimal solution is Lyapunov-stable.