Iterative methods for nonlinear equations and their semilocal convergence  

作　　者：Liang CHEN Chuanqing GU Lin ZHENG 

机构地区：[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

出　　处：《Frontiers of Mathematics in China》2023年第2期105-124,共20页中国高等学校学术文摘·数学（英文）

摘　　要：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.

关 键 词：Nonlinear equation numerical method semilocal convergence Newton method Banach space 

分 类 号：O221[理学—运筹学与控制论]