On the convergence of generalized polynomial chaos expansions

On the Convergence of Generalized Polynomial Chaos Expansions

A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which im...

polynomial chaos expansions KEVIN

Submitted for the MAR13 Meeting of The American Physical Society Simulation of stochastic quantum systems using polynomial chaos expansions KEVIN YOUNG, MATTHEW GRACE, Sandia National Laboratories — We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertain...

Convergence of Generalized Eigenfunction Expansions

We present a simplified theory of generalized eigenfunction expansions for a commuting family of bounded operators and with finitely many unbounded operators. We also study the convergence of these expansions, giving an abstract type of uniform convergence result, and illustrate the theory by giving two examples: The Fourier transform on Hecke operators, and the Laplacian operators in hyperboli...

Polynomial Chaos Expansions For Damped Oscillators

Uncertainty quantification is the state-of-the-art framework dealing with uncertainties arising in all kind of real-life problems. One of the framework’s functions is to propagate uncertainties from the stochastic input factors to the output quantities of interest, hence the name uncertainty propagation. To this end, polynomial chaos expansions (PCE) have been effectively used in a wide variety...

Classification Algorithms based on Generalized Polynomial Chaos