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Convergence analysis on a class of improved Chebyshev methods for nonlinear equations in Banach spaces

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  • Xiuhua Wang
  • Jisheng Kou

Abstract

In this paper, we study the semilocal convergence on a class of improved Chebyshev methods for solving nonlinear equations in Banach spaces. Different from the results for Chebyshev method considered in Hernández and Salanova (J Comput Appl Math 126:131–143, 2000 ), these methods are free from the second derivative, the R-order of convergence is also improved. We prove a convergence theorem to show the existence-uniqueness of the solution. Under the convergence conditions used in Hernández and Salanova (J Comput Appl Math 126:131–143, 2000 ), the R-order for this class of methods is proved to be at least $$3+2p$$ 3 + 2 p , which is higher than the ones of Chebyshev method considered in Hernández and Salanova (J Comput Appl Math 126:131–143, 2000 ) and the variant of Chebyshev method considered in Hernández (J Optim Theory Appl 104(3): 501–515, 2000 ) under the same conditions. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Xiuhua Wang & Jisheng Kou, 2015. "Convergence analysis on a class of improved Chebyshev methods for nonlinear equations in Banach spaces," Computational Optimization and Applications, Springer, vol. 60(3), pages 697-717, April.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:3:p:697-717
    DOI: 10.1007/s10589-014-9684-6
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    References listed on IDEAS

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    1. M. Powell, 2012. "On the convergence of trust region algorithms for unconstrained minimization without derivatives," Computational Optimization and Applications, Springer, vol. 53(2), pages 527-555, October.
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