Bounds for the Positive Eigenvectors of Nonnegative Matrices and for their Approximations by Decomposition

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Bounds for the Positive Eigenvectors of Nonnegative Matrices and for their Approximations by Decomposition

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Journal of the ACM (JACM) archive
Volume 31 , Issue 4 (October 1984) table of contents

Pages: 804 - 825

Year of Publication: 1984

ISSN:0004-5411

Authors

P.-J. Courtois
P Semal

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 11, Downloads (12 Months): 99, Citation Count: 17

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references cited by index terms review collaborative colleagues

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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	BAUER, F. L., DEUTSCn, E., AND STOER, J.Abschatzungen fur die Eigenwerte Positaver Linearer Operatoren. Lm. Alg Appl. 2 (1969), 275-302.
	2	BERMAN, A., AND PLEMMONS, R. J.Nonnegative Matrices m the Mathematical Sciences. Academic Press, New York, 1979.
	3	CHUNG, K. L.Markov Chains wtth Stanonary Transmon Probabilities. Springer-Verlag, New York, 1967.
	4	COURIOIS, P.-j.Decomposability: Queueing and Computer System Application. Academic Press, New York, I977.
	5	COURTOIS, P.-J. Error analys~s in nearly-completely decomposable stochastic systems. Econometnca 43 (1975), 691-709.
	6	COURTOtS, P. J., AND SEMAL, P.On polyhedra of Perron-Frobenius eigenveetors. Res. Rep. M 72, Philips Research Laboratory, Brussels, Belgium, Dec. 1983.
	7	SIMON, H. A., AND ANDO, A.Aggregation of variables in dynamic systems. Econometrica 29 (1961), 111-138.
	8	G. W. Stewart, Computable Error Bounds for Aggregated Markov Chains, Journal of the ACM (JACM), v.30 n.2, p.271-285, April 1983 [doi>10.1145/322374.322377]
	9	VANTILBORGH, H.The error ofaggregatmn. A contributmn to the theory of decomposable systems and applications. Doctoral thesis, Univ. Catholique de Louvain, Louvain, Belgium, 1981.

CITED BY 18

	Edmundo de Souza e Silva , Pedro Mejiá Ochoa, State space exploration in Markov models, ACM SIGMETRICS Performance Evaluation Review, v.20 n.1, p.152-166, June 1992
	Stephanie Mahévas , Gerardo Rubino, Bound Computation of Dependability and Performance Measures, IEEE Transactions on Computers, v.50 n.5, p.399-413, May 2001
	Francesco Marinuzzi , Stefano Soliani, LISA: A new symbolic package for the definition, analysis and resolution of Markovian processes: symbolic and inductive techniques, Papers from the international symposium on Symbolic and algebraic computation, p.303-311, July 27-29, 1992, Berkeley, California, United States
	Juan A. Carrasco , Javier Escribá , Angel Calderón, Efficient exploration of availability models guided by failure distances, ACM SIGMETRICS Performance Evaluation Review, v.24 n.1, p.242-251, May 1996
	P. J. Courtois, On time and space decomposition of complex structures, Communications of the ACM, v.28 n.6, p.590-603, June 1985
	Paul Skelly , Mischa Schwartz , Sudhir Dixit, A histogram-based model for video traffic behavior in an ATM multiplexer, IEEE/ACM Transactions on Networking (TON), v.1 n.4, p.446-459, Aug. 1993
	R. R. Muntz , E. de Souza e Silva , A. Goyal, Bounding availability of repairable computer systems, ACM SIGMETRICS Performance Evaluation Review, v.17 n.1, p.29-38, May 1989
	John C. S. Lui , Richard R. Muntz, Computing bounds on steady state availability of repairable computer systems, Journal of the ACM (JACM), v.41 n.4, p.676-707, July 1994
	Pierre Semal, Refinable Bounds for Large Markov Chains, IEEE Transactions on Computers, v.44 n.10, p.1216-1222, October 1995
	Peter Buchholz, An iterative bounding method for stochastic automata networks, Performance Evaluation, v.49 n.1-4, p.211-226, September 2002
	G. Iazeolla , F. Marinuzzi, LISPACK-A Methodology and Tool for the Performance Analysis of Parallel Systems and Algorithms, IEEE Transactions on Software Engineering, v.19 n.5, p.486-502, May 1993
	R. R. Muntz , E. de Souza e Silva , A. Goyal, Bounding Availability of Repairable Systems, IEEE Transactions on Computers, v.38 n.12, p.1714-1723, December 1989
	Peter Buchholz, An improved method for bounding stationary measures of finite Markov processes, Performance Evaluation, v.62 n.1-4, p.349-365, October 2005
	Peter Buchholz, Bounding stationary results of Tandem networks with MAP input and PH service time distributions, ACM SIGMETRICS Performance Evaluation Review, v.34 n.1, June 2006
	Ana Bušić , Jean-Michel Fourneau, Bounds based on lumpable matrices for partially ordered state space, Proceeding from the 2006 workshop on Tools for solving sturctured Markov chains, p.4-es, October 10-10, 2006, Pisa, Italy
	Tuǧrul Dayar , Nihal Pekergin , Sana Younès, Conditional steady-state bounds for a subset of states in Markov chains, Proceeding from the 2006 workshop on Tools for solving sturctured Markov chains, p.3-es, October 10-10, 2006, Pisa, Italy
	Mouad Ben Mamoun , Ana Bušić , Nihal Pekergin, Generalized Class 𝒞 Markov Chains And Computation Of Closed-Form Bounding Distributions, Probability in the Engineering and Informational Sciences, v.21 n.2, p.235-260, April 2007
	P. I. Pignal, An analysis of hardware and software availability exemplified on the IBM 3725 communication controller, IBM Journal of Research and Development, v.32 n.2, p.268-278, March 1988

INDEX TERMS

Classification:
G. Mathematics of Computing
G.1 NUMERICAL ANALYSIS
G.1.3 Numerical Linear Algebra
Subjects: Eigenvalues and eigenvectors (direct and iterative methods)

General Terms:
Performance, Theory, Verification

REVIEW

"Robert James Plemmons : Reviewer"

The authors use the theory of nonnegative matrices to obtain upper and lower bounds on the Perron vector of irreducible nonnegative matrices, such as those arising in the study of discrete ergodic Markov chains. The interest here is in bounding more...

Collaborative Colleagues:

P.-J. Courtois: colleagues

P Semal: colleagues

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