[PDF][PDF] FNFT: A software library for computing nonlinear Fourier transforms

S Wahls, S Chimmalgi, PJ Prins - Journal of Open Source Software, 2018 - joss.theoj.org
The conventional Fourier transform was originally developed in order to solve the heat
equation, which is a standard example for a linear evolution equation. Nonlinear Fourier …

Fast and backward stable computation of roots of polynomials, Part II: Backward error analysis; companion matrix and companion pencil

JL Aurentz, T Mach, L Robol, R Vandebril… - SIAM Journal on Matrix …, 2018 - SIAM
This work is a continuation of work by JL Aurentz, T. Mach, R. Vandebril, and DS Watkins, J.
Matrix Anal. Appl., 36 (2015), pp. 942--973. In that paper we introduced a companion QR …