Iterative methods for nonlinear equations and their semilocal convergence

doi:10.3868/s140-DDD-023-0010-x

Front. Math. China

2023, Vol. 18

Issue (2) : 105-124 https://doi.org/10.3868/s140-DDD-023-0010-x

SURVEY　ARTICLE

Iterative methods for nonlinear equations and their semilocal convergence

Liang CHEN^1,²(

), Chuanqing GU², Lin ZHENG^2,³

¹. School of Mathematics Sciences, Huaibei Normal University, Huaibei 235000, China
². Department of Mathematics, Shanghai University, Shanghai 200444, China
³. Institute of Statistics and Applied Mathematics, Anhui University of Finance & Economics, Bengbu 233030, China

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Abstract

We are concerned with the numerical methods for nonlinear equation and their semilocal convergence in this paper. The construction techniques of iterative methods are induced by using linear approximation, integral interpolation, Adomian series decomposition, Taylor expansion, multi-step iteration, etc. The convergent conditions and proof methods, including majorizing sequences and recurrence relations, in semilocal convergence of iterative methods for nonlinear equations are discussed in the theoretical analysis. The majorizing functions, which are used in majorizing sequences, are also discussed in this paper.

Keywords Nonlinear equation numerical method semilocal convergence Newton method Banach space

Corresponding Author(s): Liang CHEN

About author:

Peng Lei and Charity Ngina Mwangi contributed equally to this work.

Online First Date: 19 October 2023 Issue Date: 13 November 2023

Cite this article:

Liang CHEN,Chuanqing GU,Lin ZHENG. Iterative methods for nonlinear equations and their semilocal convergence[J]. Front. Math. China, 2023, 18(2): 105-124.

URL:

https://academic.hep.com.cn/fmc/EN/10.3868/s140-DDD-023-0010-x
https://academic.hep.com.cn/fmc/EN/Y2023/V18/I2/105

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