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Interpolation in Polynomial Spaces of p-Degree
Phil-Alexander Hofmann, Damar Wicaksono, Michael Hecht
We recently introduced the Fast Newton Transform (FNT), an hierarchical algorithm for performing multivariate Newton interpolation in arbitrary downward closed polynomial spaces of…
Second roton feature in the strongly coupled electron liquid
Thomas M. Chuna, Jan Vorberger, Panagiotis Tolias +5
We present extensive \emph{ab initio} path integral Monte Carlo (PIMC) results for the dynamic properties of the finite temperature uniform electron gas (UEG) over a broad range of…
PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods
Alexander Benedix Robles, Phil-Alexander Hofmann, Thomas Chuna +2
Path integral Monte Carlo (PIMC) simulations are a cornerstone for studying quantum many-body systems. The analytic continuation (AC) needed to estimate dynamic quantities from the…
Accelerating Multivariate Newton Interpolation in Downward Closed Polynomial Spaces
Phil-Alexander Hofmann, Michael Hecht
We introduce the fast Newton transform (FNT), a multivariate Newton interpolation algorithm for downward closed polynomial spaces in quasi-tensorial grids. The FNT computes the New…
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…