Is there an algorithm to find complex roots of equations of high degrees? Let's suppose I'm given an even function of degree greater than 6 that does not have real roots, how am I supposed to find its complex roots efficiently? (please no trial and error methods, and methods that needs computer calculations)
(This is basically for differential equations, solving the characteristic equation)
EDIT: Something like Newton's method, https://www.wikipedia.com/en/Newton's_method