Uncertainty quantification (UQ) is increasingly critical for modelling complex systems in which input parameters or environmental conditions vary unpredictably. Polynomial chaos methods offer a ...

SIAM Journal on Numerical Analysis, Vol. 55, No. 1 (2017), pp. 63-86 (24 pages) A new space-time discontinuous Galerkin (dG) method utilizing special Trefftz polynomial basis functions is proposed and ...

We examine a new discrete method for regularizing ill-posed Volterra problems. Unlike many classical regularization techniques (such as Tikhonov regularization), this method preserves the Volterra ...

Abstract. We present a nonparametric approach based on local polynomial regression for ensemble forecast of time series. The state space is first reconstructed by embedding the univariate time series ...

We discuss the application of orthogonal polynomials to the estimation of probability density functions, particularly with regard to accessing features of a portfolio's profit/loss distribution. Such ...

After a five-year effort, a trio of mathematicians from across the country has solved a problem that has perplexed for more than 50 years. The problem, the Kadison-Singer conjecture, is a statement ...