Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak condition

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• 作者：Xiuhua Wang ; Jisheng Kou
• 关键词：Semilocal convergence ; Super ; Halley ; type method R ; order of convergence ; Nonlinear equations in Banach spaces ; Generalized weak condition
• 刊名：Numerical Algorithms
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：71
• 期：3
• 页码：567-584
• 全文大小：282 KB
• 参考文献：1.Ostrowski, A.M. Solution of Equations in Euclidean and Banach Spaces, 3rd edn. Academic Press, New York (1973)
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  14.Powell, M.J.D.: On the convergence of trust region algorithms for unconstrained minimization without derivatives. Comput Optim Appl 53, 527–555 (2012)CrossRef MathSciNet MATH
  
• 作者单位：Xiuhua Wang (1) (2)
  Jisheng Kou (1)
  
  1. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000, Hubei, China
  2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450052, China
  
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing
  Algorithms
  Mathematics
  Algebra
  Theory of Computation
  
• 出版者：Springer U.S.
• ISSN：1572-9265

文摘

In this paper, we consider the semilocal convergence of multi-point improved super-Halley-type methods in Banach space. Different from the results of super-Halley method studied in reference Gutiérrez, J.M. and Hernández, M.A. (Comput. Math. Appl. 36,1–8, 1998) these methods do not require second derivative of an operator, the R-order is improved and the convergence condition is also relaxed. We prove a convergence theorem to show existence and uniqueness of the solution.