2 citations · 2 across the 1 of their papers we have counts for
5 papers
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…
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…