Improved bounds for a condition number for Markov chains
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Publication:1434425
DOI10.1016/j.laa.2003.12.029zbMath1052.65004OpenAlexW2028710524MaRDI QIDQ1434425
Publication date: 4 August 2004
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.laa.2003.12.029
Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Numerical analysis or methods applied to Markov chains (65C40) Numerical computation of matrix norms, conditioning, scaling (65F35)
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Uses Software
Cites Work
- Derivatives of the Perron root at an essentially nonnegative matrix and the group inverse of an M-matrix
- Spatial activity allocation modelling: The dominant eigenvalue and its corresponding eigenvector
- On the first and second order derivatives of the Perron vector
- Sensitivity of the stationary distribution vector for an ergodic Markov chain
- Perturbations of matrices: A theorem on the Perron vector and its applications to input-output models
- Non-negative matrices and Markov chains. 2nd ed
- Entrywise perturbation theory for diagonally dominant M-matrices with applications
- Applications of Paz's inequality to perturbation bounds for Markov chains
- Markov chain sensitivity measured by mean first passage times
- Sensitivity of finite Markov chains under perturbation
- On a Question Concerning Condition Numbers for Markov Chains
- An Improvement of an Inequality of Fiedler Leading to a New Conjecture on Nonnegative Matrices
- Using the QR Factorization and Group Inversion to Compute, Differentiate, and Estimate the Sensitivity of Stationary Probabilities for Markov Chains
- Finite Continuous Time Markov Chains
- 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
- Sensitivity of the Stationary Distribution of a Markov Chain
- Uniform Stability of Markov Chains
- On a bound on algebraic connectivity: the case of equality
- Accuracy and Stability of Numerical Algorithms
- On the Elasticity of the Perron Root of a Nonnegative Matrix
- A divide and conquer approach to computing the mean first passage matrix for Markov chains via Perron complement reductions
- On the stability of the computation of the stationary probabilities of Markov chains using Perron complements
- Comparison of perturbation bounds for the stationary distribution of a Markov chain
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