A parallel solver for large-scale Markov chains

DOI10.1016/S0168-9274(01)00116-7zbMath0997.65006OpenAlexW2100377196MaRDI QIDQ1349139

Miroslav Tůma, Michele Benzi

Publication date: 21 May 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00116-7

zbMATH Keywords

algorithmMarkov chainsnumerical examplespreconditioningparallel computationsingular matrixapproximated inverse

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Numerical analysis or methods applied to Markov chains (65C40) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Parallel numerical computation (65Y05)

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Uses Software

• MARCA

Cites Work

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• A comparative study of sparse approximate inverse preconditioners
• Approximate inverse preconditioning in the parallel solution of sparse eigenproblems
• Incomplete Factorization of Singular M-Matrices
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• The Role of the Group Generalized Inverse in the Theory of Finite Markov Chains
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems
• A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
• Iterative Solution Methods
• Parallel Preconditioning with Sparse Approximate Inverses
• A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
• Fast wavelet iterative solvers applied to the Neumann problem
• Comparison of Partitioning Techniques for Two-Level Iterative Solvers on Large, Sparse Markov Chains
• A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
• THE ARITHMETIC MEAN METHOD FOR FINDING THE STATIONARY VECTOR OF MARKOV CHAINS
• A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method

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