Iterative aggregation/disaggregation methods for computing some characteristics of Markov chains

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2179, Issue , 2001, Pages 68-80

  Marek, Ivo ^a   Mayer, Petr ^b  

^a CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

MARKOV PROCESSES;

AGGREGATION/DISAGGREGATION; CONVERGENCE PROPERTIES; MEAN FIRST PASSAGE TIME; PROBABILITY VECTOR;

ITERATIVE METHODS;

EID: 0013405133     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45346-6_6     Document Type: Conference Paper

References (11)

1. P. J. Courtois and P. Semal. Block iterative algorithms for stochastic matrices, Linear Algebra Appl., 76, 59–80, 1986.
2. R. Koury, D. F. McAllister, and W. J. Stewart. Methods for computing stationary distributions of nearly completely decomposable Markov chains, SIAM J. Alg. Disc. Meth., 5(2), 164–186, 1984.
3. R. Koury, D. F. McAllister, and W. J. Stewart. On the Raleigh-Ritz refinement technique for nearly uncoupled stochastic matrices, Linear Algebra Appl. 60, 1–25. 1984.
4. I. Marek. Frobenius theory of positive operators. Comparison theorems and applications, SIAM J. Appl. Math. 19, 607–628, 1970.
5. I. Marek and P. Mayer. Convergence analysis of an aggregation/disaggregation iterative method for computation stationary probability vectors of stochastic matrices, Numerical Linear Algebra With Applications, 5, 253–274, 1998.
6. I. Marek and P. Mayer. Convergence theory of some classes of iterative aggregation/ disaggregation methods for computing stationary probability vectors of stochastic matrices, LAA, 2001, (submitted).
7. I. Marek and D. Szyld. Splittings of M-operators, irreducibility and the index of the iteration operators, Numer. Functional Anal. Optim., 11, 529–553, 1990.
8. J. Ortega and W. Rheinboldt. Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
9. W. J. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton, NJ., 1994.
10. H. Vantilborgh. The error aggregation. A contribution to the theory of decomposable systems and applications, PhD Thesis, Faculty of Applied Sciences, Louvain Catholic University, Louvain-la Neuve, Belgium, 1981.
11. R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1962.