Finding the largest eigenvalue of a nonnegative tensor

SIAM Journal on Matrix Analysis and Applications

Volumn 31, Issue 3, 2009, Pages 1090-1099

  Ng, Michael ^a   Qi, Liqun ^b   Zhou, Guanglu ^c  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^c CURTIN UNIVERSITY   (Australia)

Author keywords

Higher order markov chains; Iterative method; Nonnegative tensor; Spectral radius

Indexed keywords

HIGHER-ORDER MARKOV CHAINS; LARGEST EIGENVALUES; NON-NEGATIVE MATRIX; NUMERICAL RESULTS; SPECTRAL RADII;

EIGENVALUES AND EIGENFUNCTIONS; MARKOV PROCESSES; TENSORS;

ITERATIVE METHODS;

EID: 72449208683     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/09074838X     Document Type: Article

References (14)

1. A. BERMAN AND R. J. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, Classics in Appl. Math. 9, SIAM, Philadelphia, 1994.
2. K. C. CHANG, K. PEARSON AND T. ZHANG, Perron-Frobenius theorem for nonnegative tensors, Comm. Math. Sci., 6 (2008), pp. 507-520.
3. K. C. CHANG, K. PEARSON AND T. ZHANG, On eigenvalue problems of real symmetric tensors, J. Math. Anal. Appl., 350 (2009), pp. 416-422.
4. W. CHING, E. FUNG, AND M. NG, Higher-order Markov model for the Newsboy's problem, J. Oper. Res. Soc., 54 (2003), pp. 291-298.
5. W. CHING AND M. NG, Markov Chains: Models, Algorithms and Applications, Int. Ser. Oper. Res. Manag. Sci., Springer, New York, 2006.
6. L. COLLATZ, Einschliessungssatz für die charakteristischen Zahlen von Matrizen, Math. Zeit., 48 (1942), pp. 221-226.
7. L.-H. LIM, Singular values and eigenvalues of tensors: A variational approach, in Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP '05), Vol. 1, IEEE Computer Society Press, Piscataway, NJ, 2005, pp. 129-132.
8. S. NAHMIAS, Production and Operation Analysis, McGraw-Hill, Chicago, 1997.
9. L. QI, Eigenvalues of a real supersymmetric tensor, J. Symbolic Comput., 40 (2005), pp. 1302-1324.
10. L. QI, Eigenvalues and invariants of tensor, J. Math. Anal. Appl., 325 (2007), pp. 1363-1377.
11. L. QI, W. SUN, AND Y. WANG, Numerical multilinear algebra and its applications, Frontiers Math. China, 2 (2007), pp. 501-526.
12. L. QI, Y. WANG, AND E.X. WU, D-eigenvalues of diffusion kurtosis tensor, J. Comput. Appl. Math., 221 (2008), pp. 150-157.
13. R. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.
14. R. J. WOOD AND M. J. O'NEILL, Finding the spectral radius of a large sparse nonnegative matrix, ANZIAM J., 48 (2007), pp. C330-C345.