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

Abstract In this paper we study the convergence of the famous Weierstrass method for simultaneous approximation of polynomial zeros over a complete normed field. We present a new semilocal convergence theorem for the Weierstrass method under a new type of initial conditions. Our result is obtained by combining ideas of Weierstrass (1891) and Proinov (2010). A priori and a posteriori error estimates are also provided under the new initial conditions.

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