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.

引用

页码：397 / 406

页数：10

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