The Kronecker product and stochastic automata networks

Journal of Computational and Applied Mathematics

Volumn 167, Issue 2, 2004, Pages 429-447

  Langville, Amy N ^a   Stewart, William J ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Kronecker product properties; Kronecker products; Preconditioning; Stochastic automata networks

Indexed keywords

COMPUTER NETWORKS; STOCHASTIC PROGRAMMING;

KRONECKER PRODUCT; STOCHASTIC AUTOMATA NETWORKS;

AUTOMATA THEORY;

MATHEMATICAL ANALYSIS;

EID: 2442610490     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.10.010     Document Type: Article

References (23)

1. Buchholz P. Projection methods for the analysis of stochastic automata networks Plateau B. Stewart W.J. Silva M. Numerical Solution of Markov Chains 1999 149-168 Prensas Universitarias de Zaragoza
2. Campbell S.L. Meyer C.D. Generalized Inverses of Linear Transformations 1979 Pitman Publishing London
3. Fernandes P. Plateau B. Stewart W.J. Efficient descriptor-vector multiplications in stochastic automata networks J. Assoc. Comput. Mach. 45 1998 381-414
4. Graham A. Kronecker Products and Matrix Calculus with Applications 1981 Wiley New York
5. Henderson H.V. Pukelsheim F. Searle S.R. On the history of the Kronecker product Linear and Multilinear Algebra 14 1983 113-120
6. Horn R.A. Johnson C.R. Topics in Matrix Analysis 1991 Cambridge University Press Cambridge
7. A.N. Langville, Preconditioning for stochastic automata networks, Ph.D. Thesis, Operations Research Program, North Carolina State University, May 2002.
8. A.N. Langville, W.J. Stewart, A Kronecker product approximate inverse preconditioner for SANs, J. Numer. Linear Algebra Appl., to appear.
9. A.N. Langville, W.J. Stewart, Testing the NKP preconditioner on MCs and SANs, INFORMS J. Comput., to appear.
10. MacDuffee C.C. The Theory of Matrices 1946 Chelsea New York
11. Meyer C.D. Matrix Analysis and Applied Linear Algebra 2000 SIAM Philadelphia
12. Meyer C.D. The role of the group generalized inverse in the theory of finite Markov chains SIAM Rev. 17 1975 443-464
13. Pitsianis N. Van Loan C. Approximation with Kronecker products Moonen M.S. Golub G.H. Linear Algebra for Large Scale and Real Time Applications 1993 293-314 Kluwer Academic Publishers Dordrecht
14. Plateau B. On the stochastic structure of parallelism and synchronization models for distributed algorithms Performance Evaluation Rev. 13 1985 142-154
15. Plateau B. PEPS: a package for solving complex Markov models of parallel systems Puigjaner R. Potier D. Modelling Techniques and Tools for Computer Performance Evaluation 1990 291-306 Plenum Press New York
16. Plateau B. Atif K. Stochastic automata network for modelling parallel systems IEEE Trans. Software Eng. 17 10 1991 1093-1108
17. Plateau B. Fourneau J.M. A methodology for solving Markov models of parallel systems J. Parallel Distributed Comput. 12 1991 370-387
18. B. Plateau, W.J. Stewart, P. Fernandes, On the benefits of using functional transitions in Kronecker modelling, Performance Evaluation (2001), submitted.
19. Steeb W-H. Kronecker Product of Matrices and Applications 1991 Wissenschaftsverlag Mannheim
20. Stewart W.J. Introduction to the Numerical Solution of Markov Chains 1994 Princeton University Press Princeton, NJ
21. Stewart W.J. Stochastic automata networks Grassmann W.K. Computational Probability 2000 113-152 Kluwer Academic Press Boston
22. Stewart W.J. Atif K. Plateau B. The numerical solution of stochastic automata networks European J. Oper. Res. 86 1995 503-525
23. Van Loan C.F. The ubiquitous Kronecker product J. Comput. Appl. Math. 123 2000 85-100