| 非线性代数方程组求根新算法 |
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| 引用本文： | 盛平兴,汤正诠.非线性代数方程组求根新算法[J].商丘师范学院学报,2004,20(2):63-65. |
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| 作者姓名： | 盛平兴 汤正诠 |
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| 作者单位： | 上海大学理学院,数学系,上海,200436 |
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| 摘 要： | 利用动力系统中的奇点理论与最优化中极值之间的一种等价关系，来求解非线性代数方程组或函数方程组的根．我们重新论证了相应的动力系统的稳定奇点对应于辅助函数的局部极大值，附加判剐就能断定是否为非线性代数方程的根．3个实例用来检验算法的有效性．
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| 关 键 词： | 非线性代数方程组 奇点理论 最优化中极值 梯度动力系统 N元函数极值 |
| 文章编号： | 1672-3600(2004)02-0063-03 |
| 修稿时间： | 2003年6月16日 |
New algorithm on finding roots of systems of nonlinear algebraic equations |
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| SHENG Ping-xing,Tang Zheng-quan.New algorithm on finding roots of systems of nonlinear algebraic equations[J].Journal of Shangqiu Teachers College,2004,20(2):63-65. |
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| Authors: | SHENG Ping-xing Tang Zheng-quan |
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| Abstract: | This paper creates a new algorithm on finding roots of systems of nonlinear algebraic equations or functional equations via equivalence between fixed points in dynamical systems and local extreme points of function in n variables.It is verified that some local maximum points correspond to some stable equilibria of induced gradient dynamical systems.It can be checked that whether computed stable fixed points are roots of systems of nonlinear algebraic equations or not.Three examples are given to test availability of the new algorithm. |
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| Keywords: | roots of systems of nonlinear algebraic equations stable equilibrium of gradient dynamical system sufficient and necessary condition on extreme value of function in n variables numerical algorithm on ODEs |
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