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[资源] Numerical Methods for Stochastic Computations: A Spectral Method Approach

一本介绍由系数或者区域随机性所得到的随机方程的数值计算方法，包括gPC, collocation methods等等以及一些简单的应用例子。
Author: Dongbin Xiu (The University of Utah)
Publisher: Princeton University Press, Year: 2010
Preface:
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.

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附件 1 : Numerical_Methods_for_Stochastic_Computations-A_Spectral_Method_Approach.pdf

2014-07-16 16:48:07, 806.46 K