Satellite collision probability estimation using polynomial chaos expansions

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

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

Numerical Analysis, Engineering, Orthogonal Polynomials +10

The Homogeneous Chaos

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

Chaos Theory, Entropy, High-dimensional Chaos +2

Modeling uncertainty in flow simulations via generalized polynomial chaos

Dongbin Xiu, George Em Karniadakis · Journal of Computational Physics · 2003 · 1.4K citations

Engineering, Chaos Theory, Uncertainty Quantification +5

The square-root unscented Kalman filter for state and parameter-estimation

Rudolph van der Merwe, Eric A. Wan · 2002 · 1.2K citations

State Estimation, Nonlinear System Identification, Adaptive Filter +11

Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations

Ivo Babuška, Raúl Tempone, Georgios E. Zouraris · SIAM Journal on Numerical Analysis · 2004 · 840 citations

Numerical Analysis, Finite Element Method, Engineering +15