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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Prof. Yimin Wei, Fudan University

Inviter:  
Title:
Hankel Tensors: Fast Algorithms and Inheritance Properties
Time & Venue:
2017.12.20 16:00-17:00 N420
Abstract:

This talk 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.

We show that if a lower-order Hankel tensor is positive semidefinite (or positive definite, or negative semi-definite, or negative definite, or SOS), then its associated higher-order Hankel tensor with the same generating vector, where the higher order is a multiple of the lower order, is also positive semi-definite (or positive definite, or negative semi-definite, or negative definite, or SOS, respectively).

 

 

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