Table of Contents
Advances in Numerical Analysis
Volume 2014, Article ID 109525, 10 pages
http://dx.doi.org/10.1155/2014/109525
Research Article

The Perturbation Bound for the Spectral Radius of a Nonnegative Tensor

1School of Mathematical Sciences, South China Normal University, Guangzhou, China
2Department of Mathematics, Hong Kong Baptist University, Hong Kong

Received 29 March 2014; Revised 29 August 2014; Accepted 9 September 2014; Published 28 September 2014

Academic Editor: Nils Henrik Risebro

Copyright © 2014 Wen Li and Michael K. Ng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. X. Li, M. K. Ng, and Y. Ye, “HAR: hub, authority and relevance scores in multi-relational data for query search,” in Proceedings of the 12th SIAM International Conference on Data Mining (SDM '12), pp. 141–152, Anaheim, Calif, USA, April 2012. View at Scopus
  2. M. K. Ng, X. Li, and Y. Ye, “MultiRank: co-ranking for objects and relations in multi-relational data,” in Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD '11), pp. 1217–1225, August 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. L. Qi, “Eigenvalues of a real supersymmetric tensor,” Journal of Symbolic Computation, vol. 40, no. 6, pp. 1302–1324, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  4. L.-H. Lim, “Singular values and eigenvalues of tensors: a variational approach,” in Proceedings of the 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP '05), pp. 129–132, Puerto Vallarta, Mexico, December 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. K. C. Chang, K. Pearson, and T. Zhang, “Perron-Frobenius theorem for nonnegative tensors,” Communications in Mathematical Sciences, vol. 6, no. 2, pp. 507–520, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. Friedland, S. Gaubert, and L. Han, “Perron-Frobenius theorem for nonnegative multilinear forms and extensions,” Linear Algebra and its Applications, vol. 438, no. 2, pp. 738–749, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Y. Yang and Q. Yang, “Further results for Perron-Frobenius theorem for nonnegative tensors,” SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 5, pp. 2517–2530, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. K.-C. Chang, K. J. Pearson, and T. Zhang, “Primitivity, the convergence of the NQZ method, and the largest eigenvalue for nonnegative tensors,” SIAM Journal on Matrix Analysis and Applications, vol. 32, no. 3, pp. 806–819, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. Liu, G. Zhou, and N. F. Ibrahim, “An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor,” Journal of Computational and Applied Mathematics, vol. 235, no. 1, pp. 286–292, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. M. Ng, L. Qi, and G. Zhou, “Finding the largest eigenvalue of a nonnegative tensor,” SIAM Journal on Matrix Analysis and Applications, vol. 31, no. 3, pp. 1090–1099, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. L. de Lathauwer, B. de Moor, and J. Vandewalle, “A multilinear singular value decomposition,” SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 4, pp. 1253–1278, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. L. Liu and S. Y. Wang, “Sensitivity analysis of nonnegative irreducible matrices,” Applied Mathematics Letters, vol. 12, no. 2, pp. 121–124, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. K. Pearson, “Essentially positive tensors,” International Journal of Algebra, vol. 4, pp. 421–427, 2010. View at Google Scholar · View at MathSciNet
  14. J. Sun, Matrix Perturbation Analysis, Science Press, Beijing, China, 2001.