Numerical Methods for Stochastic Computations: A Spectral Method Approach Van Dongbin Xiu is an English-language textbook that delves deeply into numerical methods for stochastic computations. The book is suitable for students and researchers who want to deepen their understanding of methods for stochastic computations.
This textbook describes the fundamentals and applications of generalized polynomial chaos (gPC), an efficient spectral method for high-dimensional random spaces. The reader gains insight into the mathematical foundations, including polynomial approximation and probability theory, and learns how stochastic problems are transformed into deterministic systems via Galerkin and collocation methods.
The book covers practical examples and recent developments, such as non-Gaussian processes and stochastic collocation methods. In addition, it discusses the application of numerical methods for inverse problems and data assimilation in depth.
Numerical Methods for Stochastic Computations is a concise and complete handbook for graduate students and professionals working with numerical methods for stochastic computations in applied mathematics, computer science, and engineering.