A direct projection method for Markov chains

DOI10.1016/j.laa.2003.12.019zbMath1062.65011OpenAlexW2085455895MaRDI QIDQ1434408

Michele Benzi

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.2003.12.019

zbMATH Keywords

generalized inversesfinite Markov chainsGTH algorithmstationary vectorGaussian elimination methodProjectionsDirect solution methodNearly uncoupled chainsPurcell's methodRank-one updates

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Numerical analysis or methods applied to Markov chains (65C40)

Related Items (8)

Graphs with absorption: numerical methods for the absorption inverse and the computation of centrality measures ⋮ Performance and stability of direct methods for computing generalized inverses of the graph Laplacian ⋮ A numerical algorithm on the computation of the stationary distribution of a discrete time homogenous finite Markov chain ⋮ The computation of the mean first passage times for Markov chains ⋮ A Performance Comparison of Density-of-States Methods ⋮ AnRG-Factorization Approach for a BMAP/M/1 Generalized Processor-Sharing Queue ⋮ Stationary distributions and mean first passage times of perturbed Markov chains ⋮ Accurate calculations of stationary distributions and mean first passage times in Markov renewal processes and Markov chains

Cites Work

• On a direct method for the solution of nearly uncoupled Markov chains
• Sensitivity of the stationary distribution vector for an ergodic Markov chain
• Stationary distributions of perturbed Markov chains
• Perturbations of countable Markov chains and processes
• LU decompositions of generalized diagonally dominant matrices
• Perturbation results for nearly uncoupled Markov chains with applications to iterative methods
• Entrywise perturbation theory and error analysis for Markov chains
• A parallel solver for large-scale Markov chains
• Parallel algorithms of the Purcell method for direct solution of linear systems
• Relative-error bounds for the LU decomposition via the GTH algorithm
• Conjugate direction methods for solving systems of linear equations
• On the Sensitivity of the Solution of Nearly Uncoupled Markov Chains
• Regenerative Analysis and Steady State Distributions for 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
• Updating finite markov chains by using techniques of group matrix inversion
• Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• Computation of the stationary distribution of a markov chain
• Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems
• Sensitivity of the Stationary Distribution of a Markov Chain
• Uniform Stability of Markov Chains
• A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
• A Direct Projection Method for Sparse Linear Systems
• On the Effects of Using the Grassmann–Taksar–Heyman Method in Iterative Aggregation–Disaggregation
• A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
• Generalized Inversion of Modified Matrices
• NOTES ON THE SOLUTION OF ALGEBRAIC LINEAR SIMULTANEOUS EQUATIONS
• Methods of conjugate gradients for solving linear systems
• The Vector Method of Solving Simultaneous Linear Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A direct projection method for Markov chains