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Numerical Methods for Stochastic Computations: A Spectral Method Approach
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 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.
144 pages, Hardcover
First published July 1, 2010
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Displaying 1 of 1 review
February 6, 2013
As Prof. Karniadakis says, the book is comprehensive and short. It's ideal for a beginner in stochastic computations. It covers both necessary mathematical background and recent approaches like stochastic Galerkin and sparse grid.
The figures are chosen wisely and explanations are well written.
It is affordable to read opposite to the book by Omar Knio with the same topic.
Now, negative points:
Though the printing/binding quality is good the price is not fair. It is too much for such a short book.
There are a lot of typos in the book, sometimes misleading and distracting. Some parts are taken from author’s papers while the results are not correct.
The figures are chosen wisely and explanations are well written.
It is affordable to read opposite to the book by Omar Knio with the same topic.
Now, negative points:
Though the printing/binding quality is good the price is not fair. It is too much for such a short book.
There are a lot of typos in the book, sometimes misleading and distracting. Some parts are taken from author’s papers while the results are not correct.
Displaying 1 of 1 review