2017/06/12 by Jiawang Nie, Ke Ye, Nie, Jiawang +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Digital Filter Design and Implementation #FOS: Mathematics #Matrix Theory and Algorithms #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1706.03631
openalex publication_date 2017/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Hankel tensors are generalizations of Hankel matrices. This article studies the relations among various ranks of Hankel tensors. We give an algorithm that can compute the Vandermonde ranks and decompositions for all Hankel tensors. For a generic n-dimensional Hankel tensor of even order or order three, we prove that the the cp rank, symmetric rank, border rank, symmetric border rank, and Vandermonde rank all coincide with each other. In particular, this implies that the Comon's conjecture is true for generic Hankel tensors when the order is even or three. Some open questions are also posed.