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Incomplete Jacobian Newton method for nonlinear equations |
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| Authors: | Hao Liu Qin Ni |
| Affiliation: | aCollege of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, 210016, China bCollege of Sciences, Nanjing University of Technology, Nanjing, Jiangsu, 210009, China cCollege of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, 210016, China |
| Abstract: | This paper presents a new modified Newton method for nonlinear equations. This method uses a part of elements of the Jacobian matrix to obtain the next iteration point and is refereed to as the incomplete Jacobian Newton (IJN) method. The IJN method may be fit for solving large scale nonlinear equations with dense Jacobian. The conditions of linear, superlinear and quadratic convergence of the IJN method are given and the local convergence results are analyzed and proved. Some special IJN algorithms are designed and numerical experiments are given. The results show that the IJN method is promising. |
| Keywords: | Nonlinear equations Newton method Incomplete Jacobian Newton method Inexact Newton method Local convergence |
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