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

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

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...

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Main Authors: Sanjeev Kumar, Vinay Kanwar, Sushil Kumar Tomar, Sukhjit Singh
Format: Article
Language:English
Published: Hindawi Limited 2011-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2011/972537
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spelling doaj-d00bdce35d8c4488b3fd886cb000cfd12020-11-24T21:29:08ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/972537972537Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear EquationsSanjeev Kumar0Vinay Kanwar1Sushil Kumar Tomar2Sukhjit Singh3Department of Mathematics, Maharishi Markandeshwar University, Sadopur, Ambala, Haryana 134007, IndiaUniversity Institute of Engineering and Technology, Panjab University, Chandigarh 160 014, IndiaDepartment of Mathematics, Panjab University, Chandigarh 160 014, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab 148106, IndiaOne-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.http://dx.doi.org/10.1155/2011/972537
collection DOAJ
language English
format Article
sources DOAJ
author Sanjeev Kumar
Vinay Kanwar
Sushil Kumar Tomar
Sukhjit Singh
spellingShingle Sanjeev Kumar
Vinay Kanwar
Sushil Kumar Tomar
Sukhjit Singh
Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations
International Journal of Mathematics and Mathematical Sciences
author_facet Sanjeev Kumar
Vinay Kanwar
Sushil Kumar Tomar
Sukhjit Singh
author_sort Sanjeev Kumar
title Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations
title_short Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations
title_full Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations
title_fullStr Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations
title_full_unstemmed Geometrically Constructed Families of Newton's Method for Unconstrained Optimization and Nonlinear Equations
title_sort geometrically constructed families of newton's method for unconstrained optimization and nonlinear equations
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2011-01-01
description 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.
url http://dx.doi.org/10.1155/2011/972537
work_keys_str_mv AT sanjeevkumar geometricallyconstructedfamiliesofnewtonsmethodforunconstrainedoptimizationandnonlinearequations
AT vinaykanwar geometricallyconstructedfamiliesofnewtonsmethodforunconstrainedoptimizationandnonlinearequations
AT sushilkumartomar geometricallyconstructedfamiliesofnewtonsmethodforunconstrainedoptimizationandnonlinearequations
AT sukhjitsingh geometricallyconstructedfamiliesofnewtonsmethodforunconstrainedoptimizationandnonlinearequations
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