24 citations · 85 across the 39 of their papers we have counts for
15 papers · 1 filter
Extrapolating on Taylor Series Solutions of Homotopies with Nearby Poles
Jan Verschelde, Kylash Viswanathan
A polynomial homotopy is a family of polynomial systems in one parameter, which defines solution paths starting from known solutions and ending at solutions of a system that has to…
GPU Accelerated Newton for Taylor Series Solutions of Polynomial Homotopies in Multiple Double Precision
Jan Verschelde
A polynomial homotopy is a family of polynomial systems, typically in one parameter . Our problem is to compute power series expansions of the coordinates of the solutions in th…
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…
The Method of Gauss-Newton to Compute Power Series Solutions of Polynomial Homotopies
Nathan Bliss, Jan Verschelde
We consider the extension of the method of Gauss-Newton from complex floating-point arithmetic to the field of truncated power series with complex floating-point coefficients. With…
Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem
Danko Adrovic, Jan Verschelde
We present a polyhedral algorithm to manipulate positive dimensional solution sets. Using facet normals to Newton polytopes as pretropisms, we focus on the first two terms of a Pui…
Solving Schubert Problems with Littlewood-Richardson Homotopies
Frank Sottile, Ravi Vakil, Jan Verschelde
We present a new numerical homotopy continuation algorithm for finding all solutions to Schubert problems on Grassmannians. This Littlewood-Richardson homotopy is based on Vakil's…