45 citations · 108 across the 12 of their papers we have counts for
3 papers · 1 filter
Polyhedral Homotopies in Cox Coordinates
Timothy Duff, Simon Telen, Elise Walker +1
We introduce the Cox homotopy algorithm for solving a sparse system of polynomial equations on a compact toric variety . The algorithm lends its name from a construction, desc…
Backward Error Measures for Roots of Polynomials
Simon Telen, Sascha Timme, Marc Van Barel
We analyze different measures for the backward error of a set of numerical approximations for the roots of a polynomial. We focus mainly on the element-wise mixed backward error in…
Robust Numerical Tracking of One Path of a Polynomial Homotopy on Parallel Shared Memory Computers
Simon Telen, Marc Van Barel, Jan Verschelde
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on powe…