Numerical Methods for Stochastic Computations (eBook)

A Spectral Method Approach

Dongbin Xiu (Autor)

eBook Download: EPUB

2010
144 Seiten
Princeton University Press (Verlag)
978-1-4008-3534-8 (ISBN)

Infos

The@ first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations. The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples

Autor

Dongbin Xiu is associate professor of mathematics at Purdue University.

Produkt-Details

• Erscheint lt. Verlag: 1.7.2010
• Zusatzinfo: 50 line illus.
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Accuracy and precision • algorithm • Approximation • Approximation error • Approximation Theory • basis function • beta distribution • Big O notation • Boundary value problem • Burgers' equation • Cauchy–Schwarz inequality • central limit theorem • coefficient • Collocation method • Computation • computational mathematics • Conditional probability • continuous function • Continuous function (set theory) • Convergence of random variables • Covariance function • Covariance matrix • Curse of Dimensionality • Deterministic system • Dimension • Dimension (vector space) • Distribution Function • Eigenfunction • Eigenvalues and Eigenvectors • Equation • estimation • Estimation theory • existential quantification • Galerkin method • Gaussian process • Gaussian quadrature • Gibbs phenomenon • Hermite Polynomials • Identity matrix • Independence (probability theory) • Indicator function • Initial Condition • Jacobi polynomials • Kalman Filter • Karhunen–Loève theorem • Kullback–Leibler divergence • Lagrange polynomial • Laguerre polynomials • Legendre Polynomials • Lexicographical order • Likelihood Function • Linear space (geometry) • Marginal distribution • Measurement • Moment-generating function • Monte Carlo Method • Normal distribution • Numerical analysis • Numerical error • Numerical Integration • Observational error • orthogonality • orthogonal polynomials • Parameter • parametrization • partial differential equation • Poisson Point Process • polynomial • polynomial chaos • Prediction • Probability • Probability density function • Probability Distribution • Probability space • Probability Theory • Projection (linear algebra) • Quantity • Random field • Random Variable • Rate of Convergence • Recurrence relation • Sampling (Statistics) • scientific notation • Series expansion • Simultaneous Equations • sparse grid • Special case • spectral method • standard deviation • Statistic • stochastic • stochastic computing • Stochastic process • Stochastic Simulation • Subset • Theorem • Uncertainty • uncertainty quantification • Variable (mathematics) • Variance
• ISBN-10: 1-4008-3534-8 / 1400835348
• ISBN-13: 978-1-4008-3534-8 / 9781400835348