Convergence of Newton, Halley and Chebyshev iterative methods as methods for simultaneous determination of multiple polynomial zeros

详细信息    查看全文

• 作者：Veselina K. Kyncheva ; Viktor V. Yotov ; Stoil I. Ivanov ; ^{stoil@uni-plovdiv.bg}
• 关键词：Newton's method ; Halley's method ; Chebyshev's method ; Polynomial zeros ; Multiple zeros ; Local convergence
• 刊名：Applied Numerical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：112
• 期：Complete
• 页码：146-154
• 全文大小：310 K
• 卷排序：112

文摘

In this paper, we provide a local convergence analysis of Newton, Halley and Chebyshev iterative methods considered as methods for simultaneous determination of all multiple zeros of a polynomial f   over an arbitrary normed field KK. Convergence theorems with a priori and a posteriori error estimates for each of the proposed methods are established. The obtained results for Newton and Chebyshev methods are new even in the case of simple zeros. Three numerical examples are given to compare the convergence properties of the considered methods and to confirm the theoretical results.