Fast Hankel Tensor-Vector Products and Application to Exponential Data Fitting

Abstract

This paper is contributed to a fast algorithm for Hankel tensor-vector products. For this purpose, we first discuss a special class of Hankel tensors that can be diagonalized by the Fourier matrix, which is called \emph{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 $\mathcal{O}(m^{2}n\log mn)$ 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 as well. Finally, we apply the fast algorithm to exponential data fitting and the block version to 2D exponential data fitting for higher performance.

20 pages, 4 figures

References in corpus (2)

• Circulant Tensors with Applications to Spectral Hypergraph Theory and Stochastic Process
• Hankel Tensors: Associated Hankel Matrices and Vandermonde Decomposition

Cited by in corpus (5)

• SOS-Hankel Tensors: Theory and Application
• Positive Definiteness and Semi-Definiteness of Even Order Symmetric Cauchy Tensors
• Further Results on Cauchy Tensors and Hankel Tensors
• Centrosymmetric, Skew Centrosymmetric and Centrosymmetric Cauchy Tensors
• Positive Semi-Definiteness of Generalized Anti-Circulant Tensors