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Riemannian conjugate gradient methods for computing the extreme eigenvalues of symmetric tensors

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Abstract

In this paper, we propose two kinds of Riemannian conjugate gradient methods for computing the extreme eigenvalues of even order symmetric tensors. One is a sufficient descent Dai–Yuan type conjugate gradient method, and another is Zhu’s Riemannian nonmonotone conjugate gradient method. The global convergence of two proposed algorithms can be guaranteed, respectively. Numerical results are reported to demonstrate the feasibility and efficiency of the proposed methods.

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Acknowledgements

The authors would like to thank two reviewers for their constructive comments which lead to the improvement of this paper.

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  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Ya-qiong Wen & Wen Li

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  1. Ya-qiong Wen
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  2. Wen Li
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Correspondence to Wen Li.

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This research was supported by the National Natural Science Foundations of China (12071159, U1811464) .

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Wen, Yq., Li, W. Riemannian conjugate gradient methods for computing the extreme eigenvalues of symmetric tensors. Calcolo 59, 27 (2022). https://doi.org/10.1007/s10092-022-00471-8

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