Abstract
This paper addresses multilinear systems of equations which arise in various applications such as data mining and numerical partial differential equations. When the multilinear system under consideration involves a nonsingular \({\mathscr{M}}\)-tensor and a nonnegative right-hand side vector, it may have multiple nonnegative solutions. In this paper, we propose an algorithm which can always preserve the nonnegativity of solutions. Theoretically, we show that the sequence generated by the proposed algorithm is a nonnegative componentwise nonincreasing sequence and converges to a nonnegative solution of the system. Numerical results further support the novelty of the proposed method.
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Acknowledgements
The authors are grateful to Professor Donghui Li for his valuable comments on the convergence of our algorithm. Also, they would like to thank the referees for their close reading and valuable comments, which helped us improve the quality of this paper. H. He and C. Ling were supported in part by National Natural Science Foundation of China (Nos. 11771113 and 11971138) and Natural Science Foundation of Zhejiang Province (Nos. LY19A010019, LY20A010018, and LD19A010002).
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Bai, X., He, H., Ling, C. et al. A nonnegativity preserving algorithm for multilinear systems with nonsingular \({\mathcal M}\)-tensors. Numer Algor 87, 1301–1320 (2021). https://doi.org/10.1007/s11075-020-01008-2
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DOI: https://doi.org/10.1007/s11075-020-01008-2