G.W. Stewart, W.J. Stewart and D.F. McAllister. A two stage iteration for solving nearly uncoupled Markov chains. IMA Volumes in Mathematics and its Applications, Vol. 60, Recent Advances in Iterative Methods, pp. 201-216, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... GammaE t Gamma1;t GammaE t1 Delta Delta Delta Delta GammaE t;t Gamma1 B tt 1 C C C C A : 3) We discuss how accurately we can expect to solve the NUMC and show how this can be applied to aggregation disaggregation methods for these problems. Stewart, Stewart, and McAllister[12,6] have shown that such methods converge very quickly for the NUMC. Quite recently, O Cinneide[9] has shown that the variant of Gaussian elimination due to Grassman, Taksar, and Heyman[5] obtains small relative errors in the components of p for all irreducible, acyclic Markov chains, thus satisfying ....

..... t; j 6= i satisfies the hypothesis of Theorem 2.1. Then we can use our perturbation theory to insure that there is a reasonable solution to (1) 2) The stopping criteria (27) 29) could be used with almost any iterative method that is coupled with an aggregation step, for instance, that in [12,6], provided that the aggregation conforms with the pattern of near uncoupling . Note that p satisfies (A DeltaA) p = 0 c T p = 1 where k DeltaB ii k 1 ffi B . Thus p satisfies the hypothesis of Theorem 2.1 and y satisfies the hypothesis of Theorem 2.2. Equations (27) 29) is a simple ....

G.W. Stewart, W.J. Stewart, and D.F. McAllister. A two-stage iteration for solving nearly uncoupled Markov chains. Technical Report CSC TR138, Department of Computer Science, University of Maryland, College Park, MD, April 1984.

....to the analysis of computer systems. Currently, there is a very large research effort being devoted to these methods, by many different research groups. See, for example, 4] 7] 8] 9] 10] 12] 15] 16] 23] 24] 30] 31] 32] 33] 35] 36] 39] 47] 48] 49] 52] [53], 55] 61] 62] 64] and [70] With the advent of parallel and distributed computing systems, their advantages are immediately obvious. Ideally the problem is broken into subproblems that can be solved independently and the global solution obtained by pasting together the subproblem ....

G.W. Stewart, W.J. Stewart and D.F. McAllister. A two stage iteration for solving nearly uncoupled Markov chains. IMA Volumes in Mathematics and its Applications, Vol. 60, Recent Advances in Iterative Methods, pp. 201-216, 1993.

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