General convergence theorems for iterative processes and applications to the Weierstrass root-finding method

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• 作者：Petko D. Proinov ^{proinov@uni-plovdiv.bg" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Iterative methods ; Cone metric space ; Convergence analysis ; Error estimates ; Weierstrass method ; Polynomial zeros
• 刊名：Journal of Complexity
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：33
• 期：Complete
• 页码：118-144
• 全文大小：504 K

文摘

In this paper, we prove some general convergence theorems for the Picard iteration in cone metric spaces over a solid vector space. As an application, we provide a detailed convergence analysis of the Weierstrass iterative method for computing all zeros of a polynomial simultaneously. These results improve and generalize existing ones in the literature.