Data-driven polynomial chaos expansions: A weighted least-square approximation

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Dongbin Xiu, George Em Karniadakis · SIAM Journal on Scientific Computing · 2002 · 4.7K citations

Natural Sciences, Computational Engineering, Mathematics +16

The Homogeneous Chaos

Norbert Wiener · American Journal of Mathematics · 1938 · 3K citations

Calculation of Gauss quadrature rules

Gene H. Golub, John H. Welsch · Mathematics of Computation · 1969 · 1.6K citations

Computing, Computer Science, Algorithms +15

High-Order Collocation Methods for Differential Equations with Random Inputs

Dongbin Xiu, Jan S. Hesthaven · SIAM Journal on Scientific Computing · 2005 · 1.5K citations · Full text

Computing, Computational Engineering, Finite Element Analysis +15

A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

Ivo Babuška, Fabio Nobile, Raúl Tempone · SIAM Journal on Numerical Analysis · 2007 · 1.4K citations · Full text

Computing, Computational Engineering, Probability Theory +16