Incomplete Jacobian Newton method for nonlinear equations

Authors:
Hao Liu;Qin Ni
Affiliations:
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, 210016, China and College of Sciences, Nanjing University of Technology, Nanjing, Jiangsu ...;College of Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, 210016, China
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 2
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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.