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,附加判别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.
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.
出处
《商丘师范学院学报》
CAS
2004年第2期63-65,共3页
Journal of Shangqiu Normal University
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
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
