Polynomial Chaos Expansions
gPC, Wiener–Hermite expansions, and stochastic Galerkin methods.
Polynomial Chaos Expansions. gPC, Wiener–Hermite expansions, and stochastic Galerkin methods.
Foundations and canonical references
The standard treatments of polynomial chaos expansions approach the subject from complementary angles. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach (2010) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Ghanem, Stochastic Finite Elements: A Spectral Approach (2003) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for polynomial chaos expansions include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2010Numerical Methods for Stochastic Computations: A Spectral Method Approachxiu-2010
- textbook · primary · 2003Stochastic Finite Elements: A Spectral Approachghanem-2003, spanos-2003
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