Iterative Methods for Computing Stationary Distributions of Nearly Completely Decomposable Markov Chains

DOI10.1137/0605019zbMath0605.60064OpenAlexW2147581228WikidataQ56559887 ScholiaQ56559887MaRDI QIDQ3742447

D. F. McAllister, J. R. Koury, William J. Stewart

Publication date: 1984

Published in: SIAM Journal on Algebraic Discrete Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0605019

zbMATH Keywords

point and block iterative methodscomputing the stationary probability vector of a finite ergodic Markov chainnearly completely decomposable Markov chains

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Probabilistic methods, stochastic differential equations (65C99)

Related Items (18)

Iterative aggregation/disaggregation methods for computing some characteristics of Markov chains. II: Fast convergence ⋮ Block iterative algorithms for stochastic matrices ⋮ Comparacion numerica de algoritmos para calcular distribuciones estacionarias de cadenas de Markov finitas ⋮ Two queues with weighted one-way overflow ⋮ Aggregation Methods for Computing Steady States in Statistical Physics ⋮ Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes ⋮ An iterative aggregation/disaggregation procedure for modelling the long-term behaviour of continuous-time evanescent random processes ⋮ Fast multilevel methods for Markov chains ⋮ Models of perishable queueing-inventory systems with server vacations ⋮ Further Comparisons of Direct Methods for Computing Stationary Distributions of Markov Chains ⋮ Aggregation/disaggregation iterative methods applied to Leontev systems and Markov chains. ⋮ Iterant recombination with one-norm minimization for multilevel Markov chain algorithms via the ellipsoid method ⋮ Convergent Iterations for Computing Stationary Distributions of Markov Chains ⋮ On a Rayleigh-Ritz refinement technique for nearly uncoupled stochastic matrices ⋮ Estimating equilibrium probabilities for band diagonal Markov chains using aggregation and disaggregation techniques ⋮ Reduction of calcium release site models via fast/slow analysis and iterative aggregation/disaggregation ⋮ Iterative algorithms for large stochastic matrices ⋮ Convergence theory of some classes of iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices

Uses Software

• HQR3
• HQR3 EXCHNG

Cites Work

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• Methods of aggregation
• Approximation of eigencharacteristics in nearly-completely decomposable stochastic systems
• A Combined Direct-Iterative Method for Certain M-Matrix Linear Systems
• Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains
• A Simultaneous Iteration Algorithm for Real Matrices
• Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models
• Approximate Analysis of General Queuing Networks
• On Approximate Computer System Models
• A Queueing Model with Finite Waiting Room and Blocking
• Error Analysis in Nearly-Completely Decomposable Stochastic Systems
• Random Injection Control of Multiprogramming in Virtual Memory
• Finite Capacity Queuing Systems with Applications in Computer Modeling
• A comparison of numerical techniques in Markov modeling
• Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions
• Aggregation of Variables in Dynamic Systems
• The Mathematical Basis of the Interpretation of Tracer Experiments in Closed Steady-State Systems

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