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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722455200
Category :
Languages : en
Pages : 28
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Book Description
We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations. Horton, Graham Langley Research Center NAS1-19480; RTOP 505-90-52-01...
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722455200
Category :
Languages : en
Pages : 28
Get Book Here
Book Description
We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle, which uses an operator-dependent coarsening, yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations. Horton, Graham Langley Research Center NAS1-19480; RTOP 505-90-52-01...
Author: Graham Horton
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Book Description
We discuss the recently introduced multilevel algorithm for the steady-state solution of Markov chains. The method is based on an aggregation principle which is well established in the literature and features a multiplicative coarse-level correction. Recursive application of the aggregation principle which uses an operator-dependent coarsening yields a multi-level method which has been shown experimentally to give results significantly faster than the typical methods currently in use. When cast as a multigrid-like method, the algorithm is seen to be a Galerkin-Full Approximation Scheme with a solution-dependent prolongation operator. Special properties of this prolongation lead to the cancellation of the computationally intensive terms of the coarse-level equations.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: National Aeronautics and Space Adm Nasa
Publisher:
ISBN: 9781729056509
Category :
Languages : en
Pages : 36
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Book Description
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. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi. Horton, Graham and Leutenegger, Scott T. Unspecified Center NAS1-19480; RTOP 505-90-52-01...
Author: Graham Horton
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 36
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Book Description
Abstract: "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 Guass-Seidel and optimal SOR algorithms for a variety of test problems. The paper also contrasts and compares the multi-level method with the iterative aggregation- disaggregation algorithm of Takahashi."
Author: Scott T. Leutenegger
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 13
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Book Description
Author: Scott T. Leutenegger
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 0
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Book Description
Abstract: "Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper we consider the performance of the Multi-Level algorithm for solving Nearly Completely Disposable (NCD) Markov chains, for which special-purpose iterative aggregation/disaggregation algorithms such as the Koury-McAllister-Stewart (KMS) method have been developed that can exploit the decomposability of the the [sic] Markov chain. We present experimental results indicating that the general-purpose Multi-Level algorithm is competitive, and can be significantly faster than the special-purpose KMS algorithm when Gauss-Seidel and Gaussian Elimination are used for solving the individual blocks."
Author: William J. Stewart
Publisher: Springer Science & Business Media
ISBN: 1461522412
Category : Mathematics
Languages : en
Pages : 605
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Book Description
Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January 16--18, 1995, in Raleigh, North Carolina. New developments of particular interest include recent work on stability and conditioning, Krylov subspace-based methods for transient solutions, quadratic convergent procedures for matrix geometric problems, further analysis of the GTH algorithm, the arrival of stochastic automata networks at the forefront of modelling stratagems, and more. An authoritative overview of the field for applied probabilists, numerical analysts and systems modelers, including computer scientists and engineers.
Author: Julio B. Clempner
Publisher: Springer Nature
ISBN: 3031435753
Category : Technology & Engineering
Languages : en
Pages : 340
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Book Description
This book considers a class of ergodic finite controllable Markov's chains. The main idea behind the method, described in this book, is to develop the original discrete optimization problems (or game models) in the space of randomized formulations, where the variables stand in for the distributions (mixed strategies or preferences) of the original discrete (pure) strategies in the use. The following suppositions are made: a finite state space, a limited action space, continuity of the probabilities and rewards associated with the actions, and a necessity for accessibility. These hypotheses lead to the existence of an optimal policy. The best course of action is always stationary. It is either simple (i.e., nonrandomized stationary) or composed of two nonrandomized policies, which is equivalent to randomly selecting one of two simple policies throughout each epoch by tossing a biased coin. As a bonus, the optimization procedure just has to repeatedly solve the time-average dynamic programming equation, making it theoretically feasible to choose the optimum course of action under the global restriction. In the ergodic cases the state distributions, generated by the corresponding transition equations, exponentially quickly converge to their stationary (final) values. This makes it possible to employ all widely used optimization methods (such as Gradient-like procedures, Extra-proximal method, Lagrange's multipliers, Tikhonov's regularization), including the related numerical techniques. In the book we tackle different problems and theoretical Markov models like controllable and ergodic Markov chains, multi-objective Pareto front solutions, partially observable Markov chains, continuous-time Markov chains, Nash equilibrium and Stackelberg equilibrium, Lyapunov-like function in Markov chains, Best-reply strategy, Bayesian incentive-compatible mechanisms, Bayesian Partially Observable Markov Games, bargaining solutions for Nash and Kalai-Smorodinsky formulations, multi-traffic signal-control synchronization problem, Rubinstein's non-cooperative bargaining solutions, the transfer pricing problem as bargaining.
Author: David E. Keyes
Publisher: SIAM
ISBN: 089871348X
Category : Mathematics
Languages : en
Pages : 330
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Book Description
This volume is one attempt to provide cross-disciplinary communication between heterogeneous computational groups developing solutions to problems of parallelization.
