基于进化策略方法求多项式的根  

Work Out the Roots of Polynomial Based on the Evolution Strategy

作　　者：曹敦虔[1] 张明[1] 

机构地区：[1]广西民族大学数学与计算机科学学院,广西南宁530006

出　　处：《广西科学》2007年第2期98-102,共5页Guangxi Sciences

摘　　要：针对传统算法如牛顿迭代法在求多项式的根的过程中,只能对某一有限的区间求出数值解,对于一个根、重根或者是选择迭代初始点等问题的解决也不是很理想的弊端,提出一种在整个实数域(或复数域)上进行求根的进化策略算法.该算法充分发挥进化策略的群体搜索和全局收敛的特性,有效的解决了传统算法在求解过程中存在迭代初值选取难的问题,而且对系数为复(实)系数的高阶多项式求根的问题同样适用.模拟实验表明,该算法收敛速度快,精度高,比一般的求多项式根的智能算法还要好,是一种求多项式根的有效方法.It can be only worked out numerical solution in some limited interval during the process of solving the roots of polynomial by some traditional algorithm, such as Newton iteration method. And there are some shortcomings in solving the problems of single root, multiple root or choosing iterated initial point. According to above disadvantages,the author of this passage puts forward to an evolutionary strategy algorithm based on working out roots on real number field. This methods makes full use of the property of evolution strategy＇s population search and overall constringency and efficiently deals with the hard problems in iteration in traditional algorithm. It is also suitable for the complex higher order polynomial roots. Simulating experiments shows that this method has high speed of constringeney and exactness and takes good advantages over the usual method of intelligent algorithms. It＇s an efficient method in working out the roots of polynomial.

关 键 词：多项式 根 高阶 进化策略 

分 类 号：O174[理学—数学] TP18[理学—基础数学]