Global convergence of the Durand-Kerner method applied to the equation \(z^ 3 = 0\)
The Durand-Kerner method for finding all the roots of a polynomial is applied to the equation \(z^3=0\). It is proved that the method is globally convergent. The behaviour of orbits with real initial values is chaotic, while the convergence with complex initial values is balanced.
scientific article; zbMATH DE number 908429