摘要: The notion of Hankel tensors is a direct generalization of Hankel matrices, which has important applications in signal processing. Similar to the rank of matrices, ranks of tensors are defined to measure the computational complexity of tensors. In this talk, we will define three ranks for Hankel tensors: cp-rank, symmetric rank and Vandermonde rank. We will show that these three notions of ranks coincide for generic order three Hankel tensors. Moreover, we will discuss an algorithm to decompose a given tensor with respect to the Vandermonde rank. If time permits, we will also exhibit some numerical examples for the decomposition.

报告人简介:  叶科，中科院数学与系统科学研究院副研究员, 2012年在德克萨斯农工(A&M)大学获得数学专业博士学位，师从Joseph M. Landsberg教授, 其后在芝加哥大学从事博士后研究工作。研究方向为应用代数/微分几何, 计算复杂度等, 在 Foundations of Computational Mathematics, SIAM Journal on Matrix Analysis,Communications in Mathematical Sciences等期刊发表多篇论文。