ANZIAM J. 46(E) pp.C732--C743, 2005.
A faster algorithm for identification of an M-Matrix
R. J. Wood | M. J. O'Neill |
Abstract
M-matrices are important in the consideration of rates of convergence of iterative methods for solving large systems of equations and are applicable in areas such as input-output systems in economic modelling, queuing theory, and engineering. The usual definition of an M-matrix has, among other requirements, that it must be non-singular and its inverse non-negative. Following Saad (2003), Young (1971) and Berman & Shaked--Monderer (2003) two more easily checked characterisations of an M-matrix are explored. These require only the evaluation of the spectral radius of an associated non-negative matrix.
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Authors
- R. J. Wood
- M. J. O'Neill
- School of Information Technology, Charles Sturt University, Bathurst, Australia. mailto:rwood@csu.edu.au
Published July 29, 2005. ISSN 1446-8735
References
- A. Berman and N. Shaked--Monderer. Completely Positive Matrices. World Scientific. New Jersey, 2003.
- Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM, Philadelphia, 2003.
- E. Senata. Non-Negative Matrices, George Allen and Unwin, London, 1973.
- G. W. Stewart. Introduction to Matrix Computations, Academic Press, New York, 1973.
- R. Varga. Matrix Iterative Analysis, Prentice-Hall Inc, Englewood Cliffs, New Jersey, 1962.
- R. J. Wood and M. J. O'Neill. An always convergent method for finding the spectral radius of a non-negative matrix, ANZIAM J., 45(E): C474--C485, 2004. http://anziamj.austms.org.au/V45/CTAC2003/Wood
- D. M. Young. Iterative Solutions of Large Linear Systems, Academic Press, New York, 1971.