In this paper, we use the conjugate gradient method with a simple line search, which can reduce the number of computations of objective functions and gradients, to compute the largest H-eigenvalue of the large-scale tensors generated from uniform directed hypergraphs. For this kind of tensor, we provide a fast tensor-vector product computing scheme, which can calculate \({\mathcal {T}}x^{k-1}\) and \({\mathcal {T}}x^{k-2}\) efficiently. The convergence of the proposed algorithm can be guaranteed. Numerical results are reported to illustrate the efficiency of our algorithm.

中文翻译：

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计算由有向超图生成的大规模张量的最大 H 特征值

在本文中，我们使用共轭梯度法和简单的线搜索，可以减少目标函数和梯度的计算次数，计算由均匀有向超图生成的大规模张量的最大 H 特征值。对于这种张量，我们提供了一种快速的张量-向量乘积计算方案，可以计算\({\mathcal {T}}x^{k-1}\)和\({\mathcal {T}}x^ {k-2}\)有效。可以保证所提出算法的收敛性。报告了数值结果以说明我们算法的效率。