Abstract
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.
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Communicated by Carlos Hoppen.
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This work was supported by the National Natural Science Foundation of China under Grants 11771210, 12001281. This work was partially supported by the Suqian Sci&Tech Program Grant Nos. Z2019110 and Z2020135.
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Zhang, X., Ni, Q., Sheng, Z. et al. Computing the largest H-eigenvalue of large-scale tensors generated from directed hypergraphs. Comp. Appl. Math. 40, 170 (2021). https://doi.org/10.1007/s40314-021-01554-y
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DOI: https://doi.org/10.1007/s40314-021-01554-y