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Tensor Methods for Solving Symmetric \({\mathcal {M}}\)-tensor Systems

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Abstract

Tensor systems involving tensor-vector products (or polynomial systems) are considered. We solve these tensor systems, especially focusing on symmetric \({\mathcal {M}}\)-tensor systems, by some tensor methods. A new tensor method is proposed based on the rank-1 approximation of the coefficient tensor. Numerical examples show that the tensor methods could be more efficient than the Newton method for some \({\mathcal {M}}\)-tensor systems.

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Acknowledgements

We would like to thank two referees for their helpful comments and Dr. Wei-Yang Ding for his useful discussions on this topic.

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Authors and Affiliations

  1. Department of Mathematics, University of Macau, Taipa, Macao, China

    Ze-Jia Xie & Xiao-Qing Jin

  2. School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, China

    Yi-Min Wei

Authors
  1. Ze-Jia Xie
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  2. Xiao-Qing Jin
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  3. Yi-Min Wei
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Correspondence to Yi-Min Wei.

Additional information

The work is supported by the research Grant MYRG2016-00077-FST from University of Macau and International Cooperation Project of Shanghai Municipal Science and Technology Commission under Grant 16510711200.

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Xie, ZJ., Jin, XQ. & Wei, YM. Tensor Methods for Solving Symmetric \({\mathcal {M}}\)-tensor Systems. J Sci Comput 74, 412–425 (2018). https://doi.org/10.1007/s10915-017-0444-5

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  • DOI: https://doi.org/10.1007/s10915-017-0444-5

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