Abstract
In 1891, Weierstrass presented his famous iterative method for finding all the zeros of a polynomial simultaneously. In this paper we establish three new local convergence theorems for the Weierstrass method with a posteriori and a priori error estimates. The main result of the paper generalizes, improves and complements some well known results of Dochev (1962), Kjurkchiev and Markov (1983) and Yakoubsohn (2002). The results are given for polynomials over an arbitrary normed field.
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