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The accelerated overrelaxation splitting method for solving symmetric tensor equations

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Abstract

This paper is concerned with solving the multilinear systems \({\mathscr {A}}\mathbf {x}^{m-1}=\mathbf {b}\) whose coefficient tensors are mth-order and n-dimensional symmetric tensors. We first extend the accelerated overrelaxation (AOR) splitting method to solve the tensor equation. To improve the convergence, we develop a Newton-AOR (NAOR) method that hybridizes the Newton method and the accelerated overrelaxation scheme. Convergence analysis shows that the proposed methods converge under appropriate assumptions. Finally, some numerical examples are provided to show the effectiveness of the methods proposed.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, People’s Republic of China

    Xin-Fang Zhang, Qing-Wen Wang & Tao Li

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  1. Xin-Fang Zhang
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  2. Qing-Wen Wang
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  3. Tao Li
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Correspondence to Qing-Wen Wang.

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Communicated by Jinyun Yuan.

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Research is supported by National Natural Science Foundation of China [Grant numbers 11971294 and 11571220].

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Zhang, XF., Wang, QW. & Li, T. The accelerated overrelaxation splitting method for solving symmetric tensor equations. Comp. Appl. Math. 39, 155 (2020). https://doi.org/10.1007/s40314-020-01182-y

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  • DOI: https://doi.org/10.1007/s40314-020-01182-y

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