A new semilocal convergence theorem for the Weierstrass method for finding zeros of a polynomial simultaneously (Q2442867)

The convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field is studied. A new semilocal convergence theorem for the Weierstrass method under a new type of initial conditions is obtained. The result is obtained by combining ideas of \textit{K. Weierstrass} [Berl. Ber. 1891, 1085--1101 (1891; JFM 23.0083.02)] and \textit{P. D. Proinov} [J. Complexity 26, No. 1, 3--42 (2010; Zbl 1185.65095)]. A priori and a posteriori error estimates are also provided under the new initial conditions.