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Semilocal convergence of a sixth-order method in Banach spaces

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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.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Lin Zheng & Chuanqing Gu

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  1. Lin Zheng
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  2. Chuanqing Gu
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Correspondence to Chuanqing Gu.

Additional information

The work are supported by Shanghai Natural Science Foundation (10ZR1410900) and by Key Disciplines of Shanghai Municipality (S30104).

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Zheng, L., Gu, C. Semilocal convergence of a sixth-order method in Banach spaces. Numer Algor 61, 413–427 (2012). https://doi.org/10.1007/s11075-012-9541-6

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  • DOI: https://doi.org/10.1007/s11075-012-9541-6

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