Finding the spectral radius of a large sparse non-negative matrix

ANZIAM Journal

Volumn 48, Issue , 2007, Pages C330-C345

  Wood, R J ^a   O'Neill, M J ^a  

^a CHARLES STURT UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70450185947     PISSN: 14461811     EISSN: 14468735     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. E. Andersson and P. Ekstrom. Investigating Google's PageRank Algorithm. Technical report, Uppsala University, 2004. http://www.it.uu.se/edu/course/homepage/projektTDB/vt04/projekt5/website/report.pdf
2. W. E. Arnoldi. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Q. Appl. Maths, 9:17-29, 1951.
3. A. Brauer. The theorems of Ledermann and Ostrowski on positive matrices. Duke Math. J., 24:265-274, 1957.
4. L. Collatz. Einschliessungenssatz für die characteristischen Zahlen von Matrizen. Math Zeit, 48:221-6, 1942.
5. G Frobenius. Uber Matrizen aus nicht negativen Elementen. Akad Wiss, Berlin, 1912.
6. G. H. Golub and C. Greif. An Arnoldi-type Algorithm for Computing PageRank, 2006. http://www.cs.ubc.ca/~greif/Papers/gg2006BIT.pdf
7. G. H. Golub and C. F. Van Loan. Matrix Computations. John Hopkins University Press, Baltimore, 1996.
8. W. Ledermann. Bounds for the greatest latent root of a positive matrix. J. London Math Soc, 25:265-268, 1950.
9. M. Lu, H. Liu, and F. Tian. A new upper bound for the Spectral Radius of graphs with girth at least 5. Lin Alg Appl, 414:512-516, 2006.
10. A. Ostrowski. Bounds for the greatest latent root of a positive matrix. J. London Math Soc, pages 253-256, 1952.
11. Y. Saad. Variations of Arnoldi's Method for computing Eigenelements of Large Unsymmetric Matrices. Lin Alg. and its Applic, 34:269-295.
12. Y. Saad. Numerical Methods for Large Eigenvalue Problems. Manchester University Press, New York, 1992.
13. 2-s Edges. Elec J. of Linear Algebra, 10:179-189, 2003.
14. G. W. Stewart. Introduction to Matrix Computations. Academic Press, New York, 1973.
15. G. W. Stewart. Simultaneous Iteration for Computing Invariant Subspaces of Non-Hermitian Matrices. Numer. Math, pages 123-136, 1976.
16. G. W. Stewart. Matrix Algorithms, volume 2: Eigensystems. SIAM, 2001.
17. R. Varga. Matrix Iterative Analysis. Prentice-Hall Inc, Englewood Cliffs, New Jersey, 1962.
18. R. J. Wood and M. J. O'Neill. Using the spectral radius to determine whether a Leontief system has a unique positive solution. Asia Pacific Journal of Operational Research, Operational Research Society of Singapore, 19:233-247, 2002.
19. R. J. Wood and M. J. O'Neill. An always convergent method for finding the spectral radius of an irreducible non-negative matrix, 2004. http://anziamj.austms.org.au/V45/CTAC2003/Wood
20. R. J. Wood and M. J. O'Neill. A faster algorithm for identification of an M-Matrix, 2005. http://anziamj.austms.org.au/V46/CTAC2004/Wood