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A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with \(\mathcal {M}\)-tensors

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Abstract

In this paper, we propose a new preconditioner of the tensor splitting iterative method for solving multi-linear systems with \(\mathcal {M}\)-tensors. We theoretically show that the spectral radii of the preconditioner iterative tensor decrease as the parameters in the new preconditioners increase, if the preconditioned tensor is a strong \(\mathcal {M}\)-tensor. Based on this, we give the comparison for spectral radii of preconditioned iterative tensors. Numerical examples are given to show our theoretical results and the efficiency of our new preconditioner. We also show the efficiency of our preconditioner used to solving higher order Markov chain.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Xinxiang, 453007, Henan, People’s Republic of China

    Lu-Bin Cui & Xiao-Qing Zhang

  2. School of Mathematics, Yunnan Normal University, Kunming, 650500, Yunnan, People’s Republic of China

    Shi-Liang Wu

Authors
  1. Lu-Bin Cui
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  2. Xiao-Qing Zhang
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  3. Shi-Liang Wu
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Correspondence to Lu-Bin Cui.

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Communicated by Jinyun Yuan.

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This document is the results of the research project funded by National Natural Science Foundations of China (Nos. 11571095, 11601134, 11961082, 17HASTIT012) and 2019 Scientific Research Project for Postgraduates of Henan Normal University(No.YL201920).

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Cui, LB., Zhang, XQ. & Wu, SL. A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with \(\mathcal {M}\)-tensors. Comp. Appl. Math. 39, 173 (2020). https://doi.org/10.1007/s40314-020-01194-8

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  • DOI: https://doi.org/10.1007/s40314-020-01194-8

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