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

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 ...

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 ...

In this paper we present the implementation of simultaneous method for the determination of polynomial roots on a distributed memory multicomputer. The total cost of such a parallelization per ...

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 ...

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 ...