The convergence ball and error analysis of the two-step Secant method

被引：3
|
作者：
Lin, Rong-fei [1 ]
Wu, Qing-biao [2 ]
Chen, Min-hong [3 ]
Khan, Yasir [2 ]
Liu, Lu [2 ]
机构：
[1] Taizhou Univ, Dept Math, Linhai 317000, Peoples R China
[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China
[3] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310012, Zhejiang, Peoples R China
来源：
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B | 2017年 / 32卷 / 04期
基金：
浙江省自然科学基金;
关键词：
two-step secant method; estimate of radius; convergence ball; Lipschitz continuous; CONTINUOUS DIVIDED DIFFERENCES; CHEBYSHEV-HALLEY METHODS; NEWTON-LIKE METHODS; BANACH-SPACES; EQUATIONS; KANTOROVICH; THEOREM;
D O I：
10.1007/s11766-017-3487-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order, we obtain an estimate of the radius of the convergence ball for the two-step secant method. Moreover, we also provide an error estimate that matches the convergence order of the two-step secant method. At last, we give an application of the proposed theorem.
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页码：397 / 406
页数：10
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