Numerical Methods for Stochastic Computations: A Spectral Method Approach

Book Details

• Author: Dongbin Xiu

• Publisher: Princeton University Press

• Language: English

• Edition: Illustrated

• ISBN: 9780691142128

• Pages: 144

• Cover: Hardcover

• Dimensions: 10.2 x 8.3 x 0.6 inches

About The Book
Numerical Methods for Stochastic Computations by Dongbin Xiu is the first graduate-level textbook focused on the fundamentals of numerical methods for stochastic computations. This concise yet comprehensive book introduces the class of numerical methods based on generalized polynomial chaos (gPC), which are fast, efficient, and accurate. These methods extend the classical spectral methods to high-dimensional random spaces and are designed to simulate complex systems subject to random inputs, making them widely applicable across various fields of computer science and engineering.

The book begins with an introduction to polynomial approximation theory and probability theory before diving into the basic theory of gPC methods. It thoroughly covers numerical examples and provides rigorous development, detailing the procedures for converting stochastic equations into deterministic ones using both the Galerkin and collocation approaches. It also addresses the challenges and distinct differences that arise from high-dimensional problems.

In the final section, the book applies gPC methods to critical areas such as inverse problems and data assimilation. Perfect for graduate students and researchers, this book serves as an ideal introduction to the field of stochastic computations, providing the tools required for advanced research. Whether used in the classroom or for self-study, this book is an essential resource for those looking to explore the complexities of stochastic computation and polynomial chaos methods.