Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative | Zendy

Yonghui Ling | Zendy; Xiubin Xu | Zendy; Shaohua Yu | Zendy

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Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative

Author(s) -

Yonghui Ling,

Xiubin Xu,

Shaohua Yu

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/682167

Subject(s) - steffensen's method , mathematics , banach space , newton's method , local convergence , convergence (economics) , fréchet derivative , operator (biology) , nonlinear system , ball (mathematics) , derivative (finance) , mathematical analysis , iterative method , newton's method in optimization , mathematical optimization , biochemistry , physics , chemistry , repressor , quantum mechanics , transcription factor , financial economics , economics , gene , economic growth

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established

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