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Hankel Tensors: Fast Algorithms and Inheritance Properties

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时间:2017-12-14  来源:数学机械化重点实验室

题目:           Hankel Tensors: Fast Algorithms and Inheritance Properties

报告人:      Yimin Wei(Professor of Fudan University)

时间地点:   2017.12.20  16:00pm  N420

摘要:          This talk is contributed to a fast algorithm for Hankel tensorvector products. First, we explain the necessity of fast algorithms for Hankel and block Hankel tensorvector 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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