Geometrically Constructed Families of Newton′s Method for Unconstrained Optimization and Nonlinear Equations | Zendy

Sanjeev Kumar | Zendy; V. Kanwar | Zendy; S. K. Tomar | Zendy; Sukhjit Singh | Zendy

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Geometrically Constructed Families of Newton′s Method for Unconstrained Optimization and Nonlinear Equations

Author(s) -

Sanjeev Kumar,

V. Kanwar,

S. K. Tomar,

Sukhjit Singh

Publication year - 2011

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2011/972537

Subject(s) - mathematics , newton's method , nonlinear system , extension (predicate logic) , newton's method in optimization , root (linguistics) , quasi newton method , iterative method , line search , mathematical optimization , local convergence , mathematical analysis , computer science , linguistics , philosophy , physics , computer security , quantum mechanics , radius , programming language

One-parameter families of Newton's iterative method for the solution of nonlinear equations and its extension to unconstrained optimization problems are presented in the paper. These methods are derived by implementing approximations through a straight line and through a parabolic curve in the vicinity of the root. The presented variants are found to yield better performance than Newton's method, in addition that they overcome its limitations

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