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

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• 作者：Petko D. Proinov ; ^{proinov@uni-plovdiv.bg" class="auth_mail} ; Milena D. Petkova ^{milenapetkova@uni-plovdiv.bg" class="auth_mail}
• 关键词：Simultaneous methods ; Weierstrass method ; Polynomial zeros ; Normed fields ; Semilocal convergence ; Error estimates
• 刊名：Journal of Complexity
• 出版年：June, 2014
• 年：2014
• 卷：30
• 期：3
• 页码：366-380
• 全文大小：417 K

文摘

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.