6 papers
How different is rational approximation from piecewise polynomial approximation?
Daan Huybrechs
The first aim of this paper is to show that there is merit to the question posed in the title. Indeed, for certain function classes, approximation by rational functions and by piec…
Compact Rational Krylov for Parametrized Systems with Application to BEM Frequency Sweeping
Kobe Bruyninckx, Daan Huybrechs, Karl Meerbergen
In parametrized linear systems the system matrix depends nonlinearly on a parameter and solutions are sought for many values o…
Function Approximation in Numerically Rank-Deficient Bases
Astrid Herremans, Daan Huybrechs
We study linear function approximation in a finite basis under finite-precision arithmetic. In a highly non-orthogonal basis, certain directions are only weakly represented, so tha…
On the algorithmic construction of deep ReLU networks
Daan Huybrechs
It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural…
Uniform H-matrix Compression with Applications to Boundary Integral Equations
Kobe Bruyninckx, Daan Huybrechs, Karl Meerbergen
Boundary integral equations lead to dense system matrices when discretized, yet they are data-sparse. Using the -matrix format, this sparsity is exploited to achieve $…
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…