Abstract
Upper and lower bounds for H-eigenvalues, Z-spectral radius and C-spectral radius of a third-order tensor are given by the minimax eigenvalue of symmetric matrices extracted from this given tensor. As applications, a sufficient condition for third-order nonsingular M-tensors and some valid sufficient conditions for the uniqueness and solvability of the solutions to multi-linear systems, tensor complementarity problems and non-homogeneous systems are proposed.
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Acknowledgements
The authors are grateful to the anonymous referees for their helpful suggestions and comments. This work is supported by Science and Technology Foundation of Guizhou Province ([2020]1Z002), Guizhou Education Department Youth Science and Technology Talents Growth Project (Grant no. QJHKYZ [2016]066) and National Natural Science Foundation of China (Grant no. 11501141).
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Communicated by Yimin Wei.
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Li, S., Chen, Z., Li, C. et al. Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices. Comp. Appl. Math. 39, 217 (2020). https://doi.org/10.1007/s40314-020-01245-0
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DOI: https://doi.org/10.1007/s40314-020-01245-0
Keywords
- H-eigenvalues
- Z-eigenvalues
- C-eigenvalues
- Nonsingular M-tensors
- Tensor complementarity problems
- Piezoelectric-type tensors