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Fast Hankel tensor–vector product and its application to exponential data fitting
Author(s) -
Ding Weiyang,
Qi Liqun,
Wei Yimin
Publication year - 2015
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1970
Subject(s) - hankel matrix , circulant matrix , mathematics , hankel transform , tensor (intrinsic definition) , tensor product , tensor contraction , exponential function , block (permutation group theory) , dimension (graph theory) , algorithm , algebra over a field , mathematical analysis , pure mathematics , fourier transform , combinatorics
Summary 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 ( m 2 n log mn ) 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.