Block iterative algorithms for stochastic matrices

DOI10.1016/0024-3795(86)90214-4zbMath0612.65020OpenAlexW1970264501WikidataQ127678948 ScholiaQ127678948MaRDI QIDQ1088381

Pierre Courtois, Pierre Semal

Publication date: 1986

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(86)90214-4

zbMATH Keywords

aggregationconvergenceregular splittingsblock Jacobi methodstationary probability distribution vectorPerron-Frobenius eigenvectorblock Gauß-Seidel methodfinite homogeneous Markov chainiterative decompositionsingular M-matricesstochastic irreducible matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Stochastic matrices (15B51) Probabilistic methods, stochastic differential equations (65C99)

Related Items (13)

A note on local and global convergence analysis of iterative aggregation-disaggregation methods. ⋮ Iterative aggregation/disaggregation methods for computing some characteristics of Markov chains. II: Fast convergence ⋮ Local convergence analysis of iterative aggregation--disaggregation methods with polynomial correction ⋮ An iterative aggregation/disaggregation procedure for modelling the long-term behaviour of continuous-time evanescent random processes ⋮ Block cyclic SOR for Markov chains with \(p\)-cyclic infinitesimal generator ⋮ Algorithms for an irreducible and lumpable strong stochastic bound ⋮ Semiconvergence of block SOR method for singular linear systems with \(p\)-cyclic matrices ⋮ Convergent Iterations for Computing Stationary Distributions of Markov Chains ⋮ A note on the extended convergence of SOR for two-periodic Markov chains ⋮ Iterative algorithms for large stochastic matrices ⋮ Guaranteed approximation of Markov chains with applications to multiplexer engineering in ATM networks ⋮ Dependability evaluation of hierarchical systems ⋮ Convergence theory of some classes of iterative aggregation/disaggregation methods for computing stationary probability vectors of stochastic matrices

Cites Work

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• Convergent nonnegative matrices and iterative methods for consistent linear systems
• Theorems on M-splittings of a singular M-Matrix which depend on graph structure
• Convergent Regular Splittings for Singular M-Matrices
• Matrix Methods for Queuing Problems
• Computable Error Bounds for Aggregated Markov Chains
• Iterative Methods for Computing Stationary Distributions of Nearly Completely Decomposable Markov Chains
• Bounds for the Positive Eigenvectors of Nonnegative Matrices and for their Approximations by Decomposition
• A chaotic asynchronous algorithm for computing the fixed point of a nonnegative matrix of unit spectral radius
• Aggregation of Variables in Dynamic Systems

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