Fast Hankel tensor-vector product and its application to exponential data fitting

SummaryThis paper is contributed to a fast algorithm for Hankel tensor–vector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensor–vector products by sketching the algorithm for both one‐dimensional and multi‐dimensional exponential data fitting. For proposing the fast algorithm, we define and investigate a special class of Hankel tensors that can be diagonalized by the Fourier matrices, which is called anti‐circulant tensors. Then, we obtain a fast algorithm for Hankel tensor–vector products by embedding a Hankel tensor into a larger anti‐circulant tensor. The computational complexity is about O(m2nlogmn) for a square Hankel tensor of order m and dimension n, and the numerical examples also show the efficiency of this scheme. Moreover, the block version for multi‐level block Hankel tensors is discussed. Copyright © 2015 John Wiley & Sons, Ltd.