New improved convergence analysis for the secant method

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• 作者：Á ; . Alberto Magre&ntilde ; á ; n^a ; ^{alberto.magrenan@unir.net" class="auth_mail" title="E-mail the corresponding author} ; Ioannis K. Argyros^b ; ^{iargyros@cameron.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Secant method ; Banach space ; Majorizing sequence ; Divided difference ; Fré ; chet-derivative
• 刊名：Mathematics and Computers in Simulation
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：119
• 期：Complete
• 页码：161-170
• 全文大小：228 K

文摘

We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center–Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies. Numerical examples validating the theoretical results are also provided in this study.