24 citations · 85 across the 39 of their papers we have counts for
4 papers · 1 filter
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 Schubert Calculus via the Littlewood-Richardson Homotopy Algorithm
Anton Leykin, Abraham Martin del Campo, Frank Sottile +2
We develop the Littlewood-Richardson homotopy algorithm, which uses numerical continuation to compute solutions to Schubert problems on Grassmannians and is based on the geometric…
PHCpack in Macaulay2
Elizabeth Gross, Sonja Petrović, Jan Verschelde
The Macaulay2 package PHCpack.m2 provides an interface to PHCpack, a general-purpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackb…
Numerical homotopies to compute generic points on positive dimensional algebraic sets
Andrew J. Sommese, Jan Verschelde
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to co…