Convergent Iterations for Computing Stationary Distributions of Markov Chains

DOI10.1137/0607044zbMath0617.65027OpenAlexW1985921170MaRDI QIDQ4727280

Robert J. Plemmons, George Phillip Barker

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1137/0607044

zbMATH Keywords

transition probability matrixMarkov chainGauss-Seidel methodJacobi methodpower methoditeration methodsgraph structureQ-matricesirreducible singular M-matricesright eigenvector

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Positive matrices and their generalizations; cones of matrices (15B48) Iterative numerical methods for linear systems (65F10) Probabilistic methods, stochastic differential equations (65C99)

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Cites Work

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• Block iterative algorithms for stochastic matrices
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• Theorems on M-splittings of a singular M-Matrix which depend on graph structure
• A Combined Direct-Iterative Method for Certain M-Matrix Linear Systems
• Convergent Regular Splittings for Singular M-Matrices
• Matrix Methods for Queuing Problems
• Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains
• On the Smallest Positive Singular Value of a Singular M-Matrix with Applications to Ergodic Markov Chains
• Iterative Methods for Computing Stationary Distributions of Nearly Completely Decomposable Markov Chains
• Incomplete Factorization of Singular M-Matrices
• A chaotic asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit spectral radius
• Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models

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