3 edition of **Projection methods for the numerical solution of Markov chain models** found in the catalog.

Projection methods for the numerical solution of Markov chain models

Y. Saad

- 216 Want to read
- 25 Currently reading

Published
**1989**
by Research Institute for Advanced Computer Science, NASA Ames Research Center, National Technical Information Service, distributor in [Moffett Field, Calif.], [Springfield, Va
.

Written in English

- Markov processes.

**Edition Notes**

Statement | Yousef Saad. |

Series | NASA contractor report -- NASA CR-188905., RIACS technical report -- 89.40., RIACS technical report -- TR 89-40. |

Contributions | Research Institute for Advanced Computer Science (U.S.) |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL15375709M |

the numerical analysis issues involved in the solution of Markov models. This introduction to Markov modeling stresses the following topics: an intuitive conceptual understanding of how system behavior can be represented with a set of states and inter-File Size: 2MB. The Propagation of Errors in the Numerical Solution of Markov Models by Brenan Joseph Mc Carragher Submitted to the Department of Aeronautics and Astronautics on in partial fulfillment of the requirements for the degree of Master of Science Abstract Equations that bound the roundoff and the integration errors incurred in the.

stead of Q in order to conform to the familiar notation of numerical linear algebra.) A number of methods, both direct and iterative, for solving (1) are surveyed by Stewart in the excellent monograph [41]. Direct solution methods for Markov chains include, besides Gaussian elimination, its variant known as . • understand the notion of a discrete-time Markov chain and be familiar with both the ﬁnite state-space case and some simple inﬁnite state-space cases, such as random walks and birth-and-death chains;File Size: KB.

packages deal with Hidden Markov Models (HMMs). In addition, the number of R packages focused on the estimation of statistical models using the Markov Chain Monte Carlo simulation approach is sensibly bigger. Finally, the msm (Jackson,), heemod (Antoine Filipovi et al.,) and theFile Size: KB. 4. Preconditioned Krylov Subspace Methods for the Numerical Solution of Markov Chains; Y. Saad. 5. A Parallel Block Projection Method of the Cimmino Type for Finite Markov Chains; M. Benzi, F. Sgallari, G. Spaletta. 6. Iterative Methods for Queueing Models with Author: William J. Stewart.

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Projection methods require finding the fixed point of an equations system which may be highly non-linear. Hence, projection methods offer no guarantee of global convergence and uniqueness of the solution.

Another family of algorithms is based on dynamic programming (DP). The DP algorithms are reliable and have desirable convergence properties.

In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and by: Get this from a library.

Projection methods for the numerical solution of Markov chain models. [Y Saad; Research Institute for Advanced Computer Science (U.S.)]. Intersecting two large research areas--numerical analysis and applied probability/quering theory--this book is a self -contained introduction to the numerical solution of structured Markov chains, which have a wide applicability in queueing theory and stochastic by: Projection methods for the numerical solution of Markov chain models / Youcef Saad --Chap.

The biconjugate gradient method for obtaining the steady-state probability distributions of Markovian multiechelon repairable item inventory systems / Donald Gross, Bingchang Gu, and Richard M. Soland --Chap. Computing the stationary distribution.

The book deals with the numerical solution of structured Markov chains which include M/G/1 and G/M/1-type Markov chains, QBD processes, non-skip-free queues, and tree-like stochastic processes and.

Finally projection methods are discussed. Projection methods are relatively recent and have proved efficient in solving Markov chains. A general projection scheme is presented in this paper along with two methods: Arnoldi's method and the generalized minimal residual's method, GMRES.

Both methods require finding an orthonormal basis 2Author: Amr Lotfy Elsayad. Kronecker structured representations are used to cope with the state space explosion problem in Markovian modeling and analysis. Currently, an open research problem is that of devising strong preconditioners to be used with projection methods for the computation of the stationary vector of Markov chains (MCs) underlying such by: Abstract: Some numerical methods for efficient implementation of the 1- and 2-factor Markov Functional models of interest rate derivatives are proposed.

These methods These methods allow a sufficiently rapid implementation of the standard calibration method, that joint calibration to caplets and swaptions becomes possible within reasonable CPU. A direct projection method for Markov chains. Stability and conditioning issues on the numerical solution of Markov chains, Ph.D.

Thesis, North Carolina State University Raleigh, NC, [12 Author: Michele Benzi. In Markov chain models, there is often a cluster of eigenv_ues very close to the unit eigenvalue, a result of the near decomposability of the system. This may render the eigenvalue methods untolerably slow.

It is important to detect such cases and use appropriate alternative decomposition methods when they arise.

2 Iterative and Direct Solution File Size: 2MB. Numerical iterative methods for Markovian dependability and performability models: new results and a comparison Performance Evaluation, Vol. 39, No. Convergence properties of Krylov subspace methods for singular linear systems with arbitrary indexCited by: Introduction to Markov chains Markov chains of M/G/1-type Algorithms for solving the power series matrix equation Quasi-Birth-Death processes Tree-like stochastic processes Numerical solution of Markov chains and queueing problems Beatrice Meini Dipartimento di Matematica, Universit`a di Pisa, Italy Computational science day, Coimbra, J File Size: 1MB.

In this chapter our attention will be devoted to computational methods for computing stationary distributions of finite irreducible Markov chains. We let q ij denote the rate at which an n -state Markov chain moves from state i to state by: The Evolution of Markov Chain Monte Carlo Methods Matthew Richey 1.

INTRODUCTION. There is an algorithm which is powerful, easy to implement, and so versatile it warrants the label “universal.” It is ﬂexible enough to solve otherwise intractable problems in physics, applied mathematics, computer science, and statistics.

A hidden Markov model is a Markov chain for which the state is only partially observable. In other words, observations are related to the state of the system, but they are typically insufficient to precisely determine the state.

Several well-known algorithms for hidden Markov models exist. Abstract. A parallel block projection method is used to approximate the stationary vector of a finite Markov chain.

Block projection methods are very attractive for solving large chains thanks to their potential for parallel computation and by: 5. [ Text Book ] [ Text Book XMARCA allows a very specific subset of the instantaneous transition, which means, as stochastic sequences of predictability (redundancy between that is published to the matrix of the Markov chain corresponds to a Markov chain are those of Technology Transfer and general purpose projection methods such as a second user written by the value of the number of states.

A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.

In continuous-time, it is known as a Markov process. It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise.

The resulting processes, which are denoted as rational processes, can be analyzed numerically like Markov chains.

If the deviation from a Markov chain is small, then most solvers for Markov models usually work also for rational processes. In other cases, specific solvers Cited by: 1. Computations with Markov Chains presents the edited and reviewed proceedings of the Second International Workshop on the Numerical Solution of Markov Chains, held January, 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 .Numerical Solution of Markov Chains.

Markov Chains are used to model processes such as behavior of queueing networks. Both the short term behavior (e.g., mean first passage times) and the long term behavior (e.g., stationary vector) are of interest, and this work has focused on both of these problems.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,in Raleigh, North Carolina.

New developments of particular interest include recent work on stability and Price: $