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math.NA2025
An Overview of Meshfree Collocation Methods
Tomas Halada, Serhii Yaskovets, Abhinav Singh +3
We provide a comprehensive overview of meshfree collocation methods for numerically approximating differential operators on continuously labeled unstructured point clouds. Meshfree…
math.NA2025
Multivariate Newton Interpolation in Downward Closed Spaces Reaches the Optimal Geometric Approximation Rates for Bos--Levenberg--Trefethen Functions
Michael Hecht, Phil-Alexander Hofmann, Damar Wicaksono +5
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runti…
math.NA2024
Multivariate Interpolation in Unisolvent Nodes -- Lifting the Curse of Dimensionality
Michael Hecht, Krzysztof Gonciarz, Jannik Michelfeit +2
We extend Newton and Lagrange interpolation to arbitrary dimensions. The core contribution that enables this is a generalized notion of non-tensorial unisolvent nodes, i.e., nodes…