Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces | Zendy

Rongfei Lin | Zendy; Yueqing Zhao | Zendy; Zdeněk Šmarda | Zendy; Yasir Khan | Zendy; Qingbiao Wu | Zendy

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Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces

Author(s) -

Rongfei Lin,

Yueqing Zhao,

Zdeněk Šmarda,

Yasir Khan,

Qingbiao Wu

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 - 10.1155/2013/923898

Subject(s) - mathematics , banach space , convergence (economics) , newton's method , type (biology) , nonlinear system , eberlein–šmulian theorem , unconditional convergence , steffensen's method , mathematical analysis , modes of convergence (annotated index) , space (punctuation) , order (exchange) , local convergence , compact convergence , pure mathematics , rate of convergence , iterative method , mathematical optimization , lp space , newton's method in optimization , computer science , key (lock) , topological vector space , isolated point , economic growth , ecology , biology , quantum mechanics , topological space , physics , finance , economics , operating system , computer security

Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples

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