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

共 50 条

[1] The convergence ball and error analysis of the two-step Secant method
LIN Rong-fei
WU Qing-biao
CHEN Min-hong
KHAN Yasir
LIU Lu
AppliedMathematics:AJournalofChineseUniversities, 2017, 32 (04) : 397 - 406
[2] The convergence ball and error analysis of the two-step Secant method
Rong-fei Lin
Qing-biao Wu
Min-hong Chen
Yasir Khan
Lu Liu
Applied Mathematics-A Journal of Chinese Universities, 2017, 32 : 397 - 406
[3] On the Convergence Ball and Error Analysis of the Modified Secant Method
Lin, Rongfei
Wu, Qingbiao
Chen, Minhong
Lei, Xuemin
ADVANCES IN MATHEMATICAL PHYSICS, 2018, 2018
[4] The Convergence Ball and Error Analysis of the Relaxed Secant Method
Lin, Rongfei
Wu, Qingbiao
Chen, Minhong
Liu, Lu
ADVANCES IN MATHEMATICAL PHYSICS, 2017, 2017
[5] HOMOCENTRIC CONVERGENCE BALL OF THE SECANT METHOD
Liang Kewei Dept.of Math.
Applied Mathematics:A Journal of Chinese Universities(Series B), 2007, (03) : 353 - 365
[6] Homocentric convergence ball of the secant method
Liang K.
Applied Mathematics-A Journal of Chinese Universities, 2007, 22 (3) : 353 - 365
[7] Two-step secant type method with approximation of the inverse operator
Shakhno, S. M.
Yarmola, H. P.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2013, 5 (01) : 150 - 155
[8] Convergence by nondiscrete mathematical induction of a two step secant's method
Amat, S.
Bermudez, C.
Busquier, S.
Gretay, J.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2007, 37 (02) : 359 - 369
[9] Error analysis in parallel two-step phase-shifting method
Anh-Hoang Phan
Piao, Mei-lan
Park, Jae-Hyeung
Kim, Nam
APPLIED OPTICS, 2013, 52 (11) : 2385 - 2393
[10] EXTENDED CONVERGENCE OF A TWO-STEP-SECANT-TYPE METHOD UNDER A RESTRICTED CONVERGENCE DOMAIN
Argyros, Ioannis K.
George, Santhosh
KRAGUJEVAC JOURNAL OF MATHEMATICS, 2021, 45 (01): : 155 - 164

← 1 2 3 4 5 →