On initial conditions for the convergence of simultaneous root finding methods (Q1924484)

This paper addresses the convergence of a number of numerical methods for the simultaneous approximation of all complex roots of a polynomial. The theorems involve only the polynomial degree and the initial approximations to the roots. The convergence theorems apply to the Weierstrass-Dichov, the Börsch-Supan-Nourein, the Maehly-Ehrlich and the square root method in ordinary complex arithmetic and to the Weierstrass interval, the Gargantini-Henrici, the Börsch-Supan-like interval, the square root interval and the Halley-like interval method in complex interval arithmetic.