Learning algebraic decompositions using Prony structures
arXiv:1907.01547 · doi:10.1016/j.aam.2020.102044
Abstract
We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for the decomposition of multivariate exponential sums, polynomials (with respect to the monomial and Chebyshev bases), Gaußian sums, spherical harmonic sums, taking also into account whether they have their support on an algebraic set.
33 pages; revised version. The third author was supported by an INdAM-DP-COFUND-2015/Marie Skłodowska-Curie Actions scholarship, grant number 713485