5 papers
Efficient Function Approximation in Enriched Approximation Spaces
Astrid Herremans, Daan Huybrechs
An enriched approximation space is the span of a conventional basis with a few extra functions included, for example to capture known features of the solution to a computational pr…
Sigmoid functions and multiscale resolution of singularities
Daan Huybrechs, Lloyd N. Trefethen
In this short, conceptual paper we observe that essentially the same mathematics applies in three contexts with disparate literatures: (1) sigmoidal and RBF approximation of smooth…
On the computation of the SVD of Fourier submatrices
Simon Dirckx, Daan Huybrechs, Robbe Ongenae
Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM Review A. Barnett has provided new bounds on the rate of ill-conditioning of…
Arbitrary-order asymptotic expansions of Gaussian quadrature rules with classical and generalised weight functions
Peter Opsomer, Daan Huybrechs
Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and expicitly list asymp…
AAA interpolation of equispaced data
Daan Huybrechs, Lloyd N. Trefethen
We propose AAA rational approximation as a method for interpolating or approximating smooth functions from equispaced data samples. Although it is always better to approximate from…