Convergent iterations for computing stationary distributions of markov
SIAM Journal on Algebraic and Discrete Methods
An iterative aggregation-disaggregation algorithm for solving linear equations
Applied Mathematics and Computation
Aggregation/disaggregation methods for computing the stationary distribution of a Markov chain
SIAM Journal on Numerical Analysis
Preconditioned conjugate gradients for solving singular systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
Computer Networks and ISDN Systems
Numerical methods in Markov chain modeling
Operations Research
Iterative aggregation/disaggregation techniques for nearly uncoupled markov chains
Journal of the ACM (JACM)
SIAM Journal on Matrix Analysis and Applications
GMRES On (Nearly) Singular Systems
SIAM Journal on Matrix Analysis and Applications
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Multilevel Solutions for Structured Markov Chains
SIAM Journal on Matrix Analysis and Applications
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Extrapolation methods for accelerating PageRank computations
WWW '03 Proceedings of the 12th international conference on World Wide Web
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
Additive Schwarz Iterations for Markov Chains
SIAM Journal on Matrix Analysis and Applications
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Efficient PageRank approximation via graph aggregation
Information Retrieval
An Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices
SIAM Journal on Scientific Computing
On the Convergence of a Class of Multilevel Methods for Large Sparse Markov Chains
SIAM Journal on Matrix Analysis and Applications
Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
SIAM Journal on Matrix Analysis and Applications
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling
An Arnoldi-Extrapolation algorithm for computing PageRank
Journal of Computational and Applied Mathematics
Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
IEEE Journal on Selected Areas in Communications
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In this paper, a theorem is presented to indicate that there exists a nonnegative constant @e=0 such that the matrix A=Q^T+@eI is a positive-definite matrix, where I@?R^n^x^n is an identity matrix and Q^T@?R^n^x^n is a matrix with positive diagonal and nonpositive off-diagonal elements. Then a class of triangular and skew-symmetric splitting (TSS) iteration method is applied to solve the positive-definite linear system Ax=b for obtaining the stationary probability vector of an irreducible Markov chain. Theoretical analyses show that the TSS iteration method converges unconditionally to the unique solution of the linear system, with the upper bound of its contraction factor dependent only on the spectrum of the triangular part and independent of the eigenvectors of the matrices involved. Moreover, the inexact triangular and skew-symmetric splitting (ITSS) iteration method, which employs certain Krylov subspace methods as the inner iteration processes at each step of the outer TSS iteration method, is proposed to accelerate the convergence of the TSS iteration method. Numerical experiments are used to illustrate the effectiveness of the TSS and ITSS iteration methods.