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Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces

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Abstract

In this paper, we study the semilocal convergence for a fifth-order method for solving nonlinear equations in Banach spaces. The semilocal convergence of this method is established by using recurrence relations. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method. As compared with the Jarratt method in Hernández and Salanova (Southwest J Pure Appl Math 1:29–40, 1999) and the Multi-super-Halley method in Wang et al. (Numer Algorithms 56:497–516, 2011), the differentiability conditions of the convergence of the method in this paper are mild and the R-order is improved. Finally, we give some numerical applications to demonstrate our approach.

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Correspondence to Chuanqing Gu.

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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. Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces. Numer Algor 59, 623–638 (2012). https://doi.org/10.1007/s11075-011-9508-z

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