We present a numerical method for utilizing stochastic models with differing fidelities to
approximate parameterized functions. A representative case is where a high-fidelity and a …

The fundamental importance of functional differential equations has been recognized in
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …

Polynomial chaos expansions (PCE) are well-suited to quantifying uncertainty in models
parameterized by independent random variables. The assumption of independence leads to …

We propose an adaptive sparse grid stochastic collocation approach based upon Leja
interpolation sequences for approximation of parameterized functions with high-dimensional …

While projection-based reduced order models can reduce the dimension of full order
solutions, the resulting reduced models may still contain terms that scale with the full order …

Polynomial approximations constructed using a least-squares approach form a ubiquitous
technique in numerical computation. One of the simplest ways to generate data for least …

The multinode Shepard operator is a linear combination of local polynomial interpolants with
inverse distance weighting basis functions. This operator can be rewritten as a blend of …

In this paper we present a quasi-optimal sample set for ordinary least squares (OLS)
regression. The quasi-optimal set is designed in such a way that, for a given number of …

Background: Computational biomedical simulations frequently contain parameters that
model physical features, material coefficients, and physiological effects, whose values are …

We construct cubature methods on scattered data via resampling on the support of known
algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF …