Introduction to the Numerical Solution of Markov Chains / / William J. Stewart.
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however...
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Superior document: | Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2021] ©1995 |
Year of Publication: | 2021 |
Language: | English |
Online Access: | |
Physical Description: | 1 online resource (561 p.) :; 41 line drawings 74 tables |
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072 | 7 | |a MAT029040 |2 bisacsh | |
082 | 0 | 4 | |a 519.2/33 |2 22 |
100 | 1 | |a Stewart, William J., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Introduction to the Numerical Solution of Markov Chains / |c William J. Stewart. |
264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2021] | |
264 | 4 | |c ©1995 | |
300 | |a 1 online resource (561 p.) : |b 41 line drawings 74 tables | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface and Acknowledgments -- |t 1. Markov Chains -- |t 2. Direct Methods -- |t 3. Iterative Methods -- |t 4. Projection Methods -- |t 5. Block Hessenberg Matrices and Solution by Recursion -- |t 6. Decompositional Methods -- |t 7. P- Cyclic Markov Chains -- |t 8. Transient Solutions -- |t 9. Stochastic Automata Networks -- |t 10. Software -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse--and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. 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 education. His efforts make for essential reading in a rapidly growing field. Here Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing methods--direct, single-and multi-vector iterative, and projection methods. More specifically, he considers recursive methods often used when the structure of the Markov chain is upper Hessenberg, iterative aggregation/disaggregation methods that are particularly appropriate when it is NCD (nearly completely decomposable), and reduced schemes for cases in which the chain is periodic. There are chapters on methods for computing transient solutions, on stochastic automata networks, and, finally, on currently available software. Throughout Stewart draws on numerous examples and comparisons among the methods he so thoroughly explains. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 29. Nov 2021) | |
650 | 0 | |a Markov processes |x Numerical solutions. | |
650 | 7 | |a MATHEMATICS / Probability & Statistics / Stochastic Processes. |2 bisacsh | |
653 | |a Absorbing state. | ||
653 | |a Arnoldi method. | ||
653 | |a Arnoldi process. | ||
653 | |a Asymptotic convergence rate. | ||
653 | |a Block Gauss-Seidel. | ||
653 | |a Block splitting. | ||
653 | |a Block triangular matrix. | ||
653 | |a Chebyshev approximation. | ||
653 | |a Coefficient matrix. | ||
653 | |a Conditional probabilities. | ||
653 | |a Conditioning. | ||
653 | |a Connected vertices. | ||
653 | |a Consistently ordered matrix. | ||
653 | |a Convergence factors. | ||
653 | |a Convergence properties. | ||
653 | |a Convergence. | ||
653 | |a Courtois problem. | ||
653 | |a Cyclic tendencies. | ||
653 | |a Decompositional methods. | ||
653 | |a Diagonal blocks. | ||
653 | |a Direct methods. | ||
653 | |a Directed graph. | ||
653 | |a Discretization parameter. | ||
653 | |a Eigenvalues. | ||
653 | |a Eigenvectors. | ||
653 | |a Ephemeral states. | ||
653 | |a Erlang law. | ||
653 | |a Euler methods. | ||
653 | |a Euler polygon. | ||
653 | |a Explicit method. | ||
653 | |a Family of solution curves. | ||
653 | |a Full pivoting. | ||
653 | |a Galerkin condition. | ||
653 | |a Gauss transformation. | ||
653 | |a Gaussian elimination. | ||
653 | |a Gerschgorin theorem. | ||
653 | |a Guard vectors. | ||
653 | |a Hermitian matrices. | ||
653 | |a Hessenberg Matrices. | ||
653 | |a Indicator function. | ||
653 | |a Iterative process. | ||
653 | |a Jacobi method. | ||
653 | |a Krylov subspace methods. | ||
653 | |a Lanczos methods. | ||
653 | |a Load-dependent. | ||
653 | |a Low-stepping transitions. | ||
653 | |a Lower Hessenberg matrix. | ||
653 | |a Machine epsilon. | ||
653 | |a Marca ordering. | ||
653 | |a Markov chains. | ||
653 | |a Memoryless property. | ||
653 | |a Near-breakdown. | ||
653 | |a Optimality property. | ||
653 | |a Orthogonal complement. | ||
653 | |a Overrelaxation. | ||
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press eBook-Package Archive 1927-1999 |z 9783110442496 |
856 | 4 | 0 | |u https://doi.org/10.1515/9780691223384?locatt=mode:legacy |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9780691223384 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9780691223384/original |
912 | |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999 |c 1927 |d 1999 | ||
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