Zobrazeno 1 - 10
of 453
pro vyhledávání: '"Huybrechs A"'
Boundary integral equation formulations of elliptic partial differential equations lead to dense system matrices when discretized, yet they are data-sparse. Using the $\mathcal{H}$-matrix format, this sparsity is exploited to achieve $\mathcal{O}(N\l
Externí odkaz:
http://arxiv.org/abs/2405.15573
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types of grading
Externí odkaz:
http://arxiv.org/abs/2312.13202
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 for scalar functions. It builds on the set-valued AAA framework introdu
Externí odkaz:
http://arxiv.org/abs/2312.10260
Autor:
Zhou, Yiqing, Huybrechs, Daan
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. The method is based on RBFs with centers on a regular grid defined o
Externí odkaz:
http://arxiv.org/abs/2308.14490
Autor:
Herremans, Astrid, Huybrechs, Daan
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 problem. Adding functions to a basis makes it overcomplete and, conseque
Externí odkaz:
http://arxiv.org/abs/2308.05652
Steepest descent methods combining complex contour deformation with numerical quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory integrals. However, unless the phase function governing the oscillation is pa
Externí odkaz:
http://arxiv.org/abs/2307.07261
Autor:
Huybrechs, Daan, Trefethen, Lloyd N.
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 functions, (2) rational approximation of analytic functions near sing
Externí odkaz:
http://arxiv.org/abs/2303.01967
Results on the rational approximation of functions containing singularities are presented. We build further on the ''lightning method'', recently proposed by Trefethen and collaborators, based on exponentially clustering poles close to the singularit
Externí odkaz:
http://arxiv.org/abs/2302.02743
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation methods using
Externí odkaz:
http://arxiv.org/abs/2211.12598
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 the discrete Fourier submatrices. In this paper we focus on the corre
Externí odkaz:
http://arxiv.org/abs/2208.12583