Certifying solutions to square systems of polynomial-exponential equations. (March 2017) - Hauenstein, Jonathan D.; Levandovskyy, Viktor
Abstract: Smale's α -theory certifies that Newton iterations will converge quadratically to a solution of a square system of analytic functions based on the Newton residual and all higher order derivatives at the given point. Shub and Smale presented a bound for the higher order derivatives of a system of polynomial equations based in part on the degrees of the equations. For a given system of polynomial-exponential equations, we consider a related system of polynomial-exponential equations and provide a bound on the higher order derivatives of this related system. This bound yields a complete algorithm for certifying solutions to polynomial-exponential systems, which is implemented inalphaCertified . Examples are presented to demonstrate this certification algorithm.