6 citations · 9 across the 5 of their papers we have counts for
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Introduction to Toric Geometry
Simon Telen
These notes are based on a series of lectures given by the author at the Max Planck Institute for Mathematics in the Sciences in Leipzig. Addressed topics include affine and projec…
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…
A Robust Numerical Path Tracking Algorithm for Polynomial Homotopy Continuation
Simon Telen, Marc Van Barel, Jan Verschelde
We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and i…
Numerical Root Finding via Cox Rings
Simon Telen
We present a new eigenvalue method for solving a system of Laurent polynomial equations defining a zero-dimensional reduced subscheme of a toric compactification of $(\mathbb{C…
Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras
Simon Telen, Bernard Mourrain, Marc Van Barel
We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a ge…