2 papers
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…