Search
Feedback
About
Help
News
| Listing 1 - 2 of 2 |
Sort by
|
Book
ISBN: 0691223386 Year: 1994 Publisher: Princeton, New Jersey ; Oxford, England : Princeton University Press,
Abstract | Keywords | Export | Availability | Bookmark
Loading...Choose an application
- Reference Manager
- EndNote
- RefWorks (Direct export to RefWorks)
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.
Markov processes --- Markov-processen. --- Numerical solutions. --- Absorbing state. --- Arnoldi method. --- Arnoldi process. --- Asymptotic convergence rate. --- Block Gauss-Seidel. --- Block splitting. --- Block triangular matrix. --- Chebyshev approximation. --- Coefficient matrix. --- Conditional probabilities. --- Conditioning. --- Connected vertices. --- Consistently ordered matrix. --- Convergence factors. --- Convergence properties. --- Convergence. --- Courtois problem. --- Cyclic tendencies. --- Decompositional methods. --- Diagonal blocks. --- Direct methods. --- Directed graph. --- Discretization parameter. --- Eigenvalues. --- Eigenvectors. --- Ephemeral states. --- Erlang law. --- Euler methods. --- Euler polygon. --- Explicit method. --- Family of solution curves. --- Full pivoting. --- Galerkin condition. --- Gauss transformation. --- Gaussian elimination. --- Gerschgorin theorem. --- Guard vectors. --- Hermitian matrices. --- Hessenberg Matrices. --- Indicator function. --- Iterative process. --- Jacobi method. --- Krylov subspace methods. --- Lanczos methods. --- Load-dependent. --- Low-stepping transitions. --- Lower Hessenberg matrix. --- Machine epsilon. --- Marca ordering. --- Markov chains. --- Memoryless property. --- Near-breakdown. --- Optimality property. --- Orthogonal complement. --- Overrelaxation.
Book
ISBN: 9780691143415 0691143412 9786612458019 1282936077 1282458019 1400833884 9781400833887 9781282458017 Year: 2010 Publisher: Princeton, N.J. : Princeton University Press,
Abstract | Keywords | Export | Availability | Bookmark
Loading...Choose an application
- Reference Manager
- EndNote
- RefWorks (Direct export to RefWorks)
This computationally oriented work describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms.
Matrices. --- Numerical analysis. --- Mathematical analysis --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Matrices --- Numerical analysis --- Algorithm. --- Analysis of algorithms. --- Analytic function. --- Asymptotic analysis. --- Basis (linear algebra). --- Basis function. --- Biconjugate gradient method. --- Bidiagonal matrix. --- Bilinear form. --- Calculation. --- Characteristic polynomial. --- Chebyshev polynomials. --- Coefficient. --- Complex number. --- Computation. --- Condition number. --- Conjugate gradient method. --- Conjugate transpose. --- Cross-validation (statistics). --- Curve fitting. --- Degeneracy (mathematics). --- Determinant. --- Diagonal matrix. --- Dimension (vector space). --- Eigenvalues and eigenvectors. --- Equation. --- Estimation. --- Estimator. --- Exponential function. --- Factorization. --- Function (mathematics). --- Function of a real variable. --- Functional analysis. --- Gaussian quadrature. --- Hankel matrix. --- Hermite interpolation. --- Hessenberg matrix. --- Hilbert matrix. --- Holomorphic function. --- Identity matrix. --- Interlacing (bitmaps). --- Inverse iteration. --- Inverse problem. --- Invertible matrix. --- Iteration. --- Iterative method. --- Jacobi matrix. --- Krylov subspace. --- Laguerre polynomials. --- Lanczos algorithm. --- Linear differential equation. --- Linear regression. --- Linear subspace. --- Logarithm. --- Machine epsilon. --- Matrix function. --- Matrix polynomial. --- Maxima and minima. --- Mean value theorem. --- Meromorphic function. --- Moment (mathematics). --- Moment matrix. --- Moment problem. --- Monic polynomial. --- Monomial. --- Monotonic function. --- Newton's method. --- Numerical integration. --- Numerical linear algebra. --- Orthogonal basis. --- Orthogonal matrix. --- Orthogonal polynomials. --- Orthogonal transformation. --- Orthogonality. --- Orthogonalization. --- Orthonormal basis. --- Partial fraction decomposition. --- Polynomial. --- Preconditioner. --- QR algorithm. --- QR decomposition. --- Quadratic form. --- Rate of convergence. --- Recurrence relation. --- Regularization (mathematics). --- Rotation matrix. --- Singular value. --- Square (algebra). --- Summation. --- Symmetric matrix. --- Theorem. --- Tikhonov regularization. --- Trace (linear algebra). --- Triangular matrix. --- Tridiagonal matrix. --- Upper and lower bounds. --- Variable (mathematics). --- Vector space. --- Weight function.
| Listing 1 - 2 of 2 |
Sort by
|