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08/28/2023
Efficient least squares approximation and collocation methods using radial basis functions
We describe an efficient method for the approximation of functions using...
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08/10/2023
Efficient Function Approximation in Enriched Approximation Spaces
An enriched approximation space is the span of a conventional basis with...
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03/03/2023
Sigmoid functions and multiscale resolution of singularities
In this short, conceptual paper we observe that essentially the same mat...
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02/06/2023
Resolution of singularities by rational functions
Results on the rational approximation of functions containing singularit...
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11/22/2022
Stable and accurate least squares radial basis function approximations on bounded domains
The computation of global radial basis function (RBF) approximations req...
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08/26/2022
On the computation of the SVD of Fourier submatrices
Contiguous submatrices of the Fourier matrix are known to be ill-conditi...
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08/24/2022
Arbitrary-order asymptotic expansions of Gaussian quadrature rules with classical and generalised weight functions
Gaussian quadrature rules are a classical tool for the numerical approxi...
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07/24/2022
AAA interpolation of equispaced data
We propose AAA rational approximation as a method for interpolating or a...
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02/11/2022
Stable approximation of Helmholtz solutions by evanescent plane waves
Solutions of the Helmholtz equation are known to be well approximated by...
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01/27/2022
An analysis of least-squares oversampled collocation methods for compactly perturbed boundary integral equations in two dimensions
In recent work (Maierhofer Huybrechs, 2022, Adv. Comput. Math.), the...
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03/31/2021
Convergence analysis of oversampled collocation boundary element methods in 2D
Collocation boundary element methods for integral equations are easier t...
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12/28/2020
Frequency extraction for BEM-matrices arising from the 3D scalar Helmholtz equation
The discretisation of boundary integral equations for the scalar Helmhol...
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10/19/2020
Quaternionic Step Derivative: Automatic Differentiation of Holomorphic Functions using Complex Quaternions
Complex Step Derivative (CSD) allows easy and accurate differentiation u...
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04/23/2020
On the adaptive spectral approximation of functions using redundant sets and frames
The approximation of smooth functions with a spectral basis typically le...
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04/07/2020
Efficient function approximation on general bounded domains using wavelets on a cartesian grid
Fourier extension is an approximation method that alleviates the periodi...
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12/20/2019
Fast hybrid numerical-asymptotic boundary element methods for high frequency screen and aperture problems based on least-squares collocation
We present a hybrid numerical-asymptotic (HNA) boundary element method (...
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12/08/2019
The AZ algorithm for least squares systems with a known incomplete generalized inverse
We introduce an algorithm for the least squares solution of a rectangula...
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11/18/2019