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math.NA2025
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…
math.NA2023
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…
math.NA2023
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…