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Semilocal Convergence Theorem for a Newton-like Method

Published online by Cambridge University Press:  07 September 2017

Rong-Fei Lin*
Affiliation:
Department of Mathematics, Taizhou University, Linhai 317000, Zhejiang, China
Qing-Biao Wu*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
Min-Hong Chen*
Affiliation:
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310012, Zhejiang, China
Lu Liu*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
Ping-Fei Dai*
Affiliation:
Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China
*
*Corresponding author. Email addresses: linrfei@tzc.edu.cn (R.-F. Lin), qbwu@zju.edu.cn (Q.-B. Wu), mhchen@zju.edu.cn (M.-H. Chen), liulu_flying@zju.edu.cn (L. Liu), pfdai@zju.edu.cn (P.-F. Dai)
*Corresponding author. Email addresses: linrfei@tzc.edu.cn (R.-F. Lin), qbwu@zju.edu.cn (Q.-B. Wu), mhchen@zju.edu.cn (M.-H. Chen), liulu_flying@zju.edu.cn (L. Liu), pfdai@zju.edu.cn (P.-F. Dai)
*Corresponding author. Email addresses: linrfei@tzc.edu.cn (R.-F. Lin), qbwu@zju.edu.cn (Q.-B. Wu), mhchen@zju.edu.cn (M.-H. Chen), liulu_flying@zju.edu.cn (L. Liu), pfdai@zju.edu.cn (P.-F. Dai)
*Corresponding author. Email addresses: linrfei@tzc.edu.cn (R.-F. Lin), qbwu@zju.edu.cn (Q.-B. Wu), mhchen@zju.edu.cn (M.-H. Chen), liulu_flying@zju.edu.cn (L. Liu), pfdai@zju.edu.cn (P.-F. Dai)
*Corresponding author. Email addresses: linrfei@tzc.edu.cn (R.-F. Lin), qbwu@zju.edu.cn (Q.-B. Wu), mhchen@zju.edu.cn (M.-H. Chen), liulu_flying@zju.edu.cn (L. Liu), pfdai@zju.edu.cn (P.-F. Dai)
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Abstract

The semilocal convergence of a third-order Newton-like method for solving nonlinear equations is considered. Under a weak condition (the so-called γ-condition) on the derivative of the nonlinear operator, we establish a new semilocal convergence theorem for the Newton-like method and also provide an error estimate. Some numerical examples show the applicability and efficiency of our result, in comparison to other semilocal convergence theorems.

Type
Research Article
Copyright
Copyright © Global-Science Press 2017 

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References

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