Citation: |
[1] |
M. Akian, S. Gaubert and A. Guterman, Tropical polyhedra are equivalent to mean payoff games, arXiv:0912.2462. |
[2] |
F. Baccelli, G. Cohen, G. J. Olsder and J. P. Quadrat, Synchronization and Linearity, Wiley Series in Probability and Mathematical Statistics, John Wiley, 1992. |
[3] |
L. Baratchart, M. Berthod and L. Pottier, Optimization of positive generalized polynomials under lpconstraints Journal of Convex Analysis, 5 (1998), 353-379. |
[4] |
L. Bloy and R. Verma, On computing the underlying fiber directions from the diffusion orientation distribution function, Medical Image Computing and Computer-Assisted Intervention MICCAI, (2008), 1-8. |
[5] |
L. Collatz, Einschliessungssatz für die charakteristischen Zahlen von Matrizen, Math. Zeit., 48 (1942), 221-226. |
[6] |
K. C. Chang, K. J. Pearson and T. Zhang, Perron-Frobenius theorem for nonnegative tensors, Commun. Math. Sci., 6 (2008), 507-520. |
[7] |
K. C. Chang, K. J. Pearson and T. Zhang, Primitivity, the convergence of the NQZ method and the largest eigenvalue for nonnegative tensors, SIAM J. Matrix Anal. Appl., 32 (2011), 806-819.doi: 10.1137/100807120. |
[8] |
K. Chang, L. Qi and G. Zhou, Singular values of a real rectangular tensor, Journal of Mathematical Analysis and Applications, 370 (2010), 284-294.doi: 10.1016/j.jmaa.2010.04.037. |
[9] |
L. De Lathauwer, B. De Moor and J. Vandewalle, On the best rank-1 and rank- (R1, ...,Rn) approximation of higher-order tensors, SIAM J. Matrix Anal. Appl., 21 (2000), 1324-1342. |
[10] |
S. Friedland, S. Gaubert and L. Han, Perron-Frobenius theorem for nonnegative multilinear forms and extensions, Linear Algebra Appl., 438 (2013), 738-749.doi: 10.1016/j.laa.2011.02.042. |
[11] |
S. Gaubert and J. Gunawardena, The Perron-Frobenius theorem for homogeneous, monotone functions, Trans. Amer. math. Soc., 356 (2004), 4931-4950.doi: 10.1090/S0002-9947-04-03470-1. |
[12] |
J. Gunawardena, From max-plus algebra to nonexpansive maps: a nonlinear theory for discrete event systems, Theoritical Computer Science, 293 (2003), 141-167.doi: 10.1016/S0304-3975(02)00235-9. |
[13] |
J. Gunawardena (editor), Idempotency, Publications of the Isaac Newton Institute, Cambridge University Press, 1998.doi: 10.1017/CBO9780511662508. |
[14] |
T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Rev., 51 (2009), 455-500.doi: 10.1137/07070111X. |
[15] |
V. N. Kolokoltsov, Nonexpansive maps and option pricing theory, Kybernetika, 34 (1998), 713-724. |
[16] |
V. N. Kolokoltsov and V. P. Maslov, Idempotency Analysis and Applications, Kluwer Academic, 1997. |
[17] |
L. H. Lim, Multilinear pagerank: measuring higher order connectivity in linked objects, The Internet: Today and Tomorrow, 2005. |
[18] |
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, 235 (2010), 286-292.doi: 10.1016/j.cam.2010.06.002. |
[19] |
M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a nonnegative tensor, SIAM J. Matrix Anal. Appl., 31 (2009), 1090-1099.doi: 10.1137/09074838X. |
[20] |
Q. Ni, L. Qi and F. Wang, An eigenvalue method for testing the positive definiteness of a multivariate form, IEEE Transactions on Automatic Control, 53 (2008), 1096-1107.doi: 10.1109/TAC.2008.923679. |
[21] |
R. D. Nussbaum, Hilbert's projective metric and iterated nonlinear maps, Mem. Amer. Math. Soc., 75 (1988).doi: 10.1090/memo/0391. |
[22] |
R. D. Nussbaum, Iterated nonlinear map and Hilbert's projective metric, II, Memoirs of the AMS, 79 (1989).doi: 10.1090/memo/0401. |
[23] |
M. Morishima, Equilibrium, Stability and Growth, Clarenson, Oxford, England, 2002. |
[24] |
L. Qi, F. Wang and Y. Wang, Z-eigenvalue methods for a global polynomial optimization problem, Mathematical Programming, 118 (2009), 301-316.doi: 10.1007/s10107-007-0193-6. |
[25] |
L. Qi , Y. Wang and E. X. Wu, D-eigenvalues of diffusion kurtosis tensor, J. Comput. Appl. Math., 221 (2008), 150-157.doi: 10.1016/j.cam.2007.10.012. |
[26] |
D. Rosenberg and S. Sorin, An operator approach to zero-sum repeated games, Israel Jurnal of Mathematics, 121 (2001), 221-246.doi: 10.1007/BF02802505. |
[27] |
R. Varga, Matrix Iterative Analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1962. |
[28] |
R. J. Wood and M. J. O'Neill, Finding the spectral radius of a large sparse non-negative matrix, Anziam J., 48 (2007), C330-C345. |
[29] |
Q. Yang and Y. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors, SIAM J. Matrix Anal. Appl., 31 (2010), 2517-2530.doi: 10.1137/090778766. |
[30] |
Q. Yang and Y. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors II, SIAM J. Matrix Anal. Appl., 32 (2011), 1236-1250.doi: 10.1137/100813671. |
[31] |
G. Zhou, L. Caccetta and L. Qi, Convergence of an algorithm for the largest singular value of a nonnegative rectangular tensor, Linear Algebra Appl., 438 (2013), 959-968.doi: 10.1016/j.laa.2011.06.038. |