PSI: Constructing ad-hoc Simplices to Interpolate High-Dimensional Unstructured Data. (arXiv:2109.13926v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Luders_S/0/1/0/all/0/1">Stefan Lüders</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Dolag_K/0/1/0/all/0/1">Klaus Dolag</a>
Interpolating unstructured data using barycentric coordinates becomes
infeasible at high dimensions due to the prohibitive memory requirements of
building a Delaunay triangulation. We present a new algorithm to construct
ad-hoc simplices that are empirically guaranteed to contain the target
coordinates, based on a nearest neighbor heuristic and an iterative
dimensionality reduction through projection. We use these simplices to
interpolate the astrophysical cooling function $Lambda$ and show that this new
approach clearly outperforms our previous implementation at high dimensions.
Interpolating unstructured data using barycentric coordinates becomes
infeasible at high dimensions due to the prohibitive memory requirements of
building a Delaunay triangulation. We present a new algorithm to construct
ad-hoc simplices that are empirically guaranteed to contain the target
coordinates, based on a nearest neighbor heuristic and an iterative
dimensionality reduction through projection. We use these simplices to
interpolate the astrophysical cooling function $Lambda$ and show that this new
approach clearly outperforms our previous implementation at high dimensions.
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