Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces | Zendy

Liang Chen | Zendy; Chuanqing Gu | Zendy; Yanfang Ma | Zendy

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Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces

Author(s) -

Liang Chen,

Chuanqing Gu,

Yanfang Ma

Publication year - 2011

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2011/786306

Subject(s) - mathematics , banach space , uniqueness , convergence (economics) , recurrence relation , a priori and a posteriori , order (exchange) , newton's method , nonlinear system , pure mathematics , mathematical analysis , philosophy , physics , epistemology , finance , quantum mechanics , economics , economic growth

We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations.The recurrence relations for the method are derived, and then an existence-uniqueness theorem is given to establish theR-order of the method to be five and a priori error bounds. Finally, a numerical application is presented to demonstrateour approach

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