17 citations · 95 across the 41 of their papers we have counts for
6 papers · 1 filter
Multivariate rational approximation of functions with curves of singularities
Nicolas Boullé, Astrid Herremans, Daan Huybrechs
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order…
QR-based Parallel Set-Valued Approximation with Rational Functions
Simon Dirckx, Karl Meerbergen, Daan Huybrechs
In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm f…
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…
Efficient least squares approximation and collocation methods using radial basis functions
Yiqing Zhou, Daan Huybrechs
We describe an efficient method for the approximation of functions using radial basis functions (RBFs), and extend this to a solver for boundary value problems on irregular domains…
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…
Resolution of singularities by rational functions
Astrid Herremans, Daan Huybrechs, Lloyd N. Trefethen
Results on the rational approximation of functions containing singularities are presented. We build further on the ''lightning method'', recently proposed by Trefethen and collabor…