| 一类新的求解非线性方程组的记忆梯度法 |
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| 引用本文： | 汤京永,董丽. 一类新的求解非线性方程组的记忆梯度法[J]. 信阳师范学院学报(自然科学版), 2011, 24(3): 311-313. DOI: 10.3969/j.issn.1003-0972.2011.03.007 |
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| 作者姓名： | 汤京永 董丽 |
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| 作者单位： | 1. 信阳师范学院数学与信意科学学院,河南信阳464000;上海交通大学数学系,上海200240
2. 信阳师范学院数学与信意科学学院,河南信阳,464000 |
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| 基金项目： | 信阳师范学院青年科研基金 |
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| 摘 要： | 提出一类新的求解非线性方程组的记忆梯度法,证明了算法的全局收敛性.该算法不依赖于问题初始点的选取,并且在迭代过程中无需计算雅克比矩阵的逆矩阵,降低了算法的计算量,节省了运算时间.与牛顿法相比,新算法更适于求解大规模非线性方程组.
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| 关 键 词： | 非线性方程组 记忆梯度法 Armijo线性搜索 全局收敛性 |
A New Memory Gradient Method for Solving Nonlinear Equations |
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| TANG Jing-yong,DONG Li. A New Memory Gradient Method for Solving Nonlinear Equations[J]. Journal of Xinyang Teachers College(Natural Science Edition), 2011, 24(3): 311-313. DOI: 10.3969/j.issn.1003-0972.2011.03.007 |
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| Authors: | TANG Jing-yong DONG Li |
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| Affiliation: | TANG Jing-yong1,2,DONG Li1(1.College of Mathematics and Information Science,Xinyang Normal University,Xinyang 464000,China,2.Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China) |
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| Abstract: | A new memory gradient method for solving nonlinear equations is presented and its global convergence is proved.The method does not depend on the initial value and is not required to calculate the inverse matrix of Jacobian matrix.By this way,the method reduces the computational amount of the algorithm and saves the computing time.It is more suitable to solve large scale nonlinear equations than the Newton's method. |
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| Keywords: | nonlinear equations memory gradient method Armijo line search global convergence |
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