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Numerical Methods for Stochastic Computations: A Spectral Method Approach,New
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The@ first graduatelevel 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 highdimensional 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 highdimensional 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 selfstudy, Numerical Methods for Stochastic Computations provides the required tools for indepth research related to stochastic computations.The first graduatelevel textbook to focus on the fundamentals of numerical methods for stochastic computationsIdeal introduction for graduate courses or selfstudyFast, efficient, and accurate numerical methodsPolynomial approximation theory and probability theory includedBasic gPC methods illustrated through examples
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- Q: What is the main focus of 'Numerical Methods for Stochastic Computations'? A: The book focuses on the fundamental aspects of numerical methods for stochastic computations, particularly emphasizing generalized polynomial chaos (gPC) methods.
- Q: Who is the author of the textbook? A: The author of the textbook is Dongbin Xiu.
- Q: What are generalized polynomial chaos (gPC) methods? A: gPC methods are fast, efficient, and accurate numerical methods used to simulate complex systems influenced by random inputs, extending classical spectral methods to high-dimensional random spaces.
- Q: What topics are covered in this textbook? A: The textbook covers polynomial approximation theory, probability theory, the theory of gPC methods, conversion of stochastic equations to deterministic ones, and applications in areas like inverse problems and data assimilation.
- Q: Is this book suitable for self-study? A: Yes, 'Numerical Methods for Stochastic Computations' is ideal for both graduate students and researchers for classroom use as well as self-study.
- Q: What kind of format does the book have? A: The book is available in hardcover format.
- Q: When was this book published? A: The book was published on July 21, 2010.
- Q: How many pages does the book contain? A: The book contains 144 pages.
- Q: What condition is the book in? A: The book is listed as 'New', indicating it is in excellent condition.
- Q: What are the key features of this textbook? A: Key features include a focus on fundamental aspects of numerical methods, an introduction to polynomial approximation and probability theory, and practical examples of gPC methods.