It is shown that no stable procedure for approximating functions from equally spaced
samples can converge exponentially for analytic functions. To avoid instability, one must …

We address classic multivariate polynomial regression tasks from a novel perspective
resting on the notion of general polynomial $ l_p $-degree, with total, Euclidean, and …

We propose an efficient surrogate modeling technique for uncertainty quantification. The
method is based on a well-known dimension-adaptive collocation scheme. We improve the …

We propose a novel numerical method based on rational spectral collocation and Clenshaw–
Curtis quadrature methods together with the “” transformation for pricing European vanilla …

The effects of random array deformations on Direction-of-Arrival (DOA) estimation with root-
Multiple Signal Classification for uniform circular arrays (UCA root-MUSIC) are characterized …

Abstract Generalized Polynomial Chaos (gPC) expansions are well established for forward
uncertainty propagation in many application areas. Although the associated computational …

We investigate the use of conformal maps for the acceleration of convergence of the
trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial …

Moving mesh methods provide an efficient way of solving partial differential equations for
which large, localised variations in the solution necessitate locally dense spatial meshes. In …

This thesis addresses surrogate modeling and forward uncertainty propagation for
parametric/stochastic versions of Maxwell's source and eigenproblem. Surrogate modeling …

The numerical evaluation of challenging integrals is a topic of interest in applied
mathematics. We investigate molecular integrals in the B function basis, an exponentially …