Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4946003 | Journal of Symbolic Computation | 2017 | 19 Pages |
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 in alphaCertified. Examples are presented to demonstrate this certification algorithm.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Jonathan D. Hauenstein, Viktor Levandovskyy,