Computable Error Bounds for Aggregated Markov Chains
- 1 April 1983
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 30 (2), 271-285
- https://doi.org/10.1145/322374.322377
Abstract
A method is described for computing the steady-state probabdlty vector of a nearly completely decomposable Markov chain The method is closely related to one proposed by Simon and Ando and developed by Courtois However, the method described here does not require the determination of a completely decomposable stochastic approximation to the transition matrix, and hence it is applicable to nonstochasttc matrices An error analysis of the procedure which results in effectively computable error bounds is gwenKeywords
This publication has 6 references indexed in Scilit:
- On the Implicit Deflation of Nearly Singular Systems of Linear EquationsSIAM Journal on Scientific and Statistical Computing, 1981
- Estimating the Largest Eigenvalue of a Positive Definite MatrixMathematics of Computation, 1979
- Exact Aggregation in Exponential Queueing NetworksJournal of the ACM, 1978
- Algorithm 506: HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix [F2]ACM Transactions on Mathematical Software, 1976
- Simultaneous iteration for computing invariant subspaces of non-Hermitian matricesNumerische Mathematik, 1976
- Error Analysis in Nearly-Completely Decomposable Stochastic SystemsEconometrica, 1975