The Fast Newton Transform (FNT)

Date

Jan 26, 2026

Time

10:00 AM - 11:00 AM

Speaker

Michael Hecht

Affiliation

University Wrocław, Helmholtz-Zentrum Dresden-Rossendorf

Language

en

Main Topic

Biologie

Host

Local Organisors: Nikola Sadovek, Maximilian Wiesmann Giulio Zucal

Description

The FNT is a novel algorithm for multivariate polynomial interpolation with a runtime of nearly Nlog(N), where N scales only sub-exponentially with spatial dimension, surpassing the runtime of the tensorial Fast Fourier Transform (FFT). We have proven and demonstrated the optimal geometric approximation rates for a class of analytic functions—termed Bos–Levenberg–Trefethen functions—to be reached by the FNT and to be maintained for the derivatives of the interpolants. This establishes the FNT as a new standard in spectral methods, particularly suitable for high-dimensional, non-periodic PDE problems, interpolation tasks, arising as the computational bottleneck in solving, e.g. 6D Boltzmann, Fokker-Planck, or Vlasov equations, multi-body Hamiltonian systems, and the inference of governing equations in complex self-organizing systems.

Last modified: Jan 15, 2026, 7:36:44 AM