Modified incomplete Jacobian Newton method for nonlinear equations

Abstract

Abstract: This paper presents a new modified Incomplete Jacobian Newton（IJN） method for nonlinear equations whose incomplete Jacobian matrix is singular in a neighborhood of exact solution. This method uses a part of elements of the Jacobian matrix and equations function to obtain the next iteration point without additional computational capacity. The numerical tests show that the modified IJN method has the same calculation efficiency with original IJN method, but more convenience and effective.

Key words: incomplete Jacobian matrix, nonlinear equations, Newton method

摘要： 在分析不精确雅可比牛顿法的基础上，进一步研究了不精确雅可比矩阵在精确解附近奇异的求解方法。利用雅可比矩阵与函数自身，在不增加新的计算量前提下，得到改进的求解非线性方程组的不精确雅可比牛顿算法。数值结果表明，改进后算法与原不精确雅可比牛顿法具有相同的计算效率，而且在使用上更为方便，有效。

关键词: 不精确雅可比矩阵, 非线性方程组, 牛顿法

CHEN Fei, WANG Haijun, CAO Suyu. Modified incomplete Jacobian Newton method for nonlinear equations[J]. Computer Engineering and Applications, 2014, 50(14): 45-47.

陈飞，王海军，曹苏玉. 求解非线性方程组的改进不精确雅可比牛顿法[J]. 计算机工程与应用, 2014, 50(14): 45-47.

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Modified incomplete Jacobian Newton method for nonlinear equations

求解非线性方程组的改进不精确雅可比牛顿法

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