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Numerical Algorithms

, Volume 61, Issue 3, pp 413–427 | Cite as

Semilocal convergence of a sixth-order method in Banach spaces

  • Lin Zheng
  • Chuanqing Gu
Original Paper

Abstract

In this paper, we introduce a new iterative method of order six and study the semilocal convergence of the method by using the recurrence relations for solving nonlinear equations in Banach spaces. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method to be six. Finally, we give some numerical applications to demonstrate our approach.

Keywords

Nonlinear equations in Banach spaces A sixth-order method Recurrence relations Semilocal convergence A priori error bounds 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina

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