Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/25566
Title: Fast Hankel tensor-vector product and its application to exponential data fitting
Authors: Ding, W
Qi, L 
Wei, Y
Keywords: Anti-circulant tensor
Block Hankel tensor
Exponential data fitting
Fast Fourier transform
Fast tensor-vector product
Hankel tensor
Higher-order singular value decomposition
Issue Date: 2015
Publisher: John Wiley & Sons
Source: Numerical linear algebra with applications, 2015 How to cite?
Journal: Numerical linear algebra with applications 
Abstract: This 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.
URI: http://hdl.handle.net/10397/25566
ISSN: 1070-5325
EISSN: 1099-1506
DOI: 10.1002/nla.1970
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