I am developing a small kinetic Monte Carlo code to study atomic evolutions in a material and need to solve several linear and non-linear equations with a high accuracy. My main issue is in finding complex roots of a non-linear equation. Which C++ library is perfect for solving a non-linear set of equations with complex roots? I am already using Eigen and Ceres in my codes, but it seems that they only can find "real" roots and not "complex" ones. All recommendations and ideas are appreciated in advance.
I mentioned that my main goal is finding "roots" and not optimization. And also, I believe that a set of equations means more than 1 equation need to be solved at a time (n equations with n variables).
(x1^2+4)+(x^2+9) ---> x1=2i & -2i and x2=3i & -3 i;
I found a Newton-like method in the following paper,