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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/972537 |
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| _version_ | 1832558962844631040 |
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| author | Sanjeev Kumar Vinay Kanwar Sushil Kumar Tomar Sukhjit Singh |
| author_facet | Sanjeev Kumar Vinay Kanwar Sushil Kumar Tomar Sukhjit Singh |
| author_sort | Sanjeev Kumar |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-d00bdce35d8c4488b3fd886cb000cfd1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d00bdce35d8c4488b3fd886cb000cfd12025-02-03T01:31:09ZengWileyInternational 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2011/972537 |
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