Multigrid methods on parallel computers—a survey of recent developments
IMPACT of Computing in Science and Engineering
Aggregation Methods for Large Markov Chains
Proceedings of the International Workshop on Computer Performance and Reliability
SPNP: Stochastic Petri Net Package
PNPM '89 The Proceedings of the Third International Workshop on Petri Nets and Performance Models
A MULTI-LEVEL SOLUTION ALGORITHM FOR STEADY-STATE MARKOV CHAINS
A MULTI-LEVEL SOLUTION ALGORITHM FOR STEADY-STATE MARKOV CHAINS
Stochastic modeling and performance evaluation for digital clock and data recovery circuits
DATE '00 Proceedings of the conference on Design, automation and test in Europe
Annals of Software Engineering
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
State Space Construction and Steady--State Solution of GSPNs on a Shared--Memory Multiprocessor
PNPM '97 Proceedings of the 6th International Workshop on Petri Nets and Performance Models
Structured analysis techniques for large Markov chains
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Algebraic Multigrid for Markov Chains
SIAM Journal on Scientific Computing
Recursively Accelerated Multilevel Aggregation for Markov Chains
SIAM Journal on Scientific Computing
Network performance engineering
Convergence of multi-level iterative aggregation-disaggregation methods
Journal of Computational and Applied Mathematics
Advances in Computational Mathematics
On-the-Fly Adaptive Smoothed Aggregation Multigrid for Markov Chains
SIAM Journal on Scientific Computing
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A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. It is shown how the well-known iterative aggregation-disaggregation algorithm of Takahashi can be interpreted as a special case of the new method.