ABSTRACT
One of the ways to find the zeros of high-degree polynomials is to use the Newton–Raphson algorithm. This is a nonlinear iterative method which, as such, needs the starting values that can be chosen randomly on the unit circle, but never on the real axis. This chapter shows the modification of the Newton–Raphson algorithm for obtaining complex roots of any function. In general, rooting a higher-degree polynomial is known to be an ill-conditioned nonlinear problem. Therefore, for high degrees it is better to use more robust methods of linear algebra. One such method is diagonalization of the Hessenberg matrix also known as the companion matrix.
