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. 54, No. 4 (2016), pp. 2256-2281 (26 pages) The focus of this paper is the approximation of analytic functions on compact intervals from their pointwise values ...

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 ...

A mathematician has uncovered a way of answering some of algebra's oldest problems. University of New South Wales Honorary Professor Norman Wildberger, has revealed a potentially game-changing ...

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 ...