3 papers
math.NA2024
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…
cs.MS2024
Extrapolating Solution Paths of Polynomial Homotopies towards Singularities with PHCpack and phcpy
Jan Verschelde, Kylash Viswanathan
PHCpack is a software package for polynomial homotopy continuation, which provides a robust path tracker [Telen, Van Barel, Verschelde, SISC 2020]. This tracker computes the radius…
math.NA2024
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…