Numerical Methods for Stochastic Computations : : A Spectral Method Approach / / Dongbin Xiu.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Xiu, Dongbin,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2010]; ©2010
• Year of Publication: 2010
• Language: English
• Physical Description: 1 online resource (144 p.) :; 50 line illus.
• Other title: Frontmatter --; Contents --; Preface --; Chapter 1. Introduction --; Chapter 2. Basic Concepts of Probability Theory --; Chapter 3. Survey of Orthogonal Polynomials and Approximation Theory --; Chapter 4. Formulation of Stochastic Systems --; Chapter 5. Generalized Polynomial Chaos --; Chapter 6. Stochastic Galerkin Method --; Chapter 7. Stochastic Collocation Method --; Chapter 8. Miscellaneous Topics and Applications --; Appendix A Some Important Orthogonal Polynomials in the Askey Scheme --; Appendix B The Truncated Gaussian Model G(α, β) --; References --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400835348; 9783110442502
• DOI: 10.1515/9781400835348?locatt=mode:legacy
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Dongbin Xiu.

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