On the Smallest Positive Singular Value of a Singular M-Matrix with Applications to Ergodic Markov Chains

DOI10.1137/0607047zbMath0599.65027OpenAlexW2084037953MaRDI QIDQ3734978

Jesse L. Barlow

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1137/0607047

zbMATH Keywords

Markov chainssingular value decompositioncondition numbersingular matrices

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (3)

Perturbation results for nearly uncoupled Markov chains with applications to iterative methods ⋮ On a direct method for the solution of nearly uncoupled Markov chains ⋮ Convergent Iterations for Computing Stationary Distributions of Markov Chains

Cites Work

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• Monitoring the stability of the triangular factorization of a sparse matrix
• Generalization of a fundamental matrix
• LU decomposition of M-matrices by elimination without pivoting
• On the LU factorization of M-matrices
• LU decompositions of generalized diagonally dominant matrices
• Generalized inverses and their application to applied probability problems
• Regular splittings and the discrete Neumann problem
• Matrix Methods for Queuing Problems
• Computable Error Bounds for Aggregated Markov Chains
• Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains
• Updating $LU$ Factorizations for Computing Stationary Distributions
• Using the QR Factorization and Group Inversion to Compute, Differentiate, and Estimate the Sensitivity of Stationary Probabilities for Markov Chains
• A Note on Monitoring the Stability of Triangular Decomposition of Sparse Matrices
• Error Analysis of Direct Methods of Matrix Inversion
• Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models
• The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Computation of the stationary distribution of a markov chain
• A comparison of numerical techniques in Markov modeling
• Computation of the stationary distribution of an infinite Markov matrix
• The Mathematical Basis of the Interpretation of Tracer Experiments in Closed Steady-State Systems

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