17 citations · 115 across the 43 of their papers we have counts for
5 papers · 1 filter
Inflation of poorly conditioned zeros of systems of analytic functions
Michael Burr, Anton Leykin
Given a system of analytic functions and an approximate zero, we introduce inflation to transform this system into one with a regular quadratic zero. This leads to a method for iso…
A search for an optimal start system for numerical homotopy continuation
Anton Leykin
We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular syste…
Certified numerical homotopy tracking
Carlos Beltrán, Anton Leykin
Given a homotopy connecting two polynomial systems we provide a rigorous algorithm for tracking a regular homotopy path connecting an approximate zero of the start system to an app…
Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions
Anton Leykin, Jan Verschelde, Ailing Zhao
Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolic-numeric deflation algorithm to restore the quadratic converg…
Newton's method with deflation for isolated singularities of polynomial systems
Anton Leykin, Jan Verschelde, Ailing Zhao
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a ne…