Aberth method

The Aberth method, also called the Aberth-Ehrlich or Ehrlich-Aberth method after Oliver Aberth and Louis W. Ehrlich, is a root-finding algorithm developed in 1967 for the simultaneous approximation of all the roots of a univariate polynomial. It converges cubically, which is an improvement over the Durand-Kerner method, another algorithm for approximating all roots at once, which converges quadratically; both algorithms converge only linearly at multiple zeros. The method is used in MPSolve, which is the reference software for approximating all roots of a polynomial to arbitrary precision.