We present the new version 2.0 of the Feynman integral reduction program Kira and
describe the new features. The primary new feature is the reconstruction of the final …

Feynman integrals are indispensable for precision calculations in quantum field theory. They
occur as soon as one goes beyond the leading order in perturbative quantum field theory …

We present the open-source C++ library FireFly for the reconstruction of multivariate rational
functions over finite fields. We discuss the involved algorithms and their implementation. As …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

We present the main improvements and new features in version 2.0 of the open-source C++
library FireFly for the interpolation of rational functions. This includes algorithmic …

We present new baby steps/giant steps algorithms of asymptotically fast running time for
dense matrix problems. Our algorithms compute the determinant, characteristic polynomial …

In this survey, we describe the classical Prony method and whose relatives. We sketch a
frequently used Prony–like method for equispaced sampled data, namely the ESPRIT …

We derive a new generalization of Prony's method to reconstruct M-sparse expansions of
(generalized) eigenfunctions of linear operators from only O (M) suitable values in a …

We consider the problem of sparse interpolation of an approximate multivariate black-box
polynomial in floating-point arithmetic. That is, both the inputs and outputs of the black-box …

Simply put, a sparse polynomial is one whose zero coefficients are not explicitly stored.
Such objects are ubiquitous in exact computing, and so naturally we would like to have …