Abstract
In this paper, we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors. Meanwhile, we show that these bounds could be tight for some special tensors. For a general nonnegative tensor which can be transformed into a matrix, we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues. Some examples are provided to show these proposed bounds greatly improve some existing ones.
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We would like to thank the referees for their helpful suggestions.
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This work is supported by the National Natural Science Foundation of China (No. 11271206) and the Natural Science Foundation of Tianjin (No. 12JCYBJC31200).
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Jia, JJ., Yang, QZ. Upper Bounds for the Spectral Radii of Nonnegative Tensors. J. Oper. Res. Soc. China 5, 83–98 (2017). https://doi.org/10.1007/s40305-016-0150-2
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DOI: https://doi.org/10.1007/s40305-016-0150-2