一种求解多项式根最大模的人工鱼群算法  

Artificial Fish School Algorithm for Finding the Largest Module of Roots of Polynomial

作　　者：王冬冬[1] 周永权[1] 

机构地区：[1]广西民族大学数学与计算机科学学院,南宁530006

出　　处：《计算机工程》2008年第7期194-196,共3页Computer Engineering

基　　金：国家自然科学基金资助项目(60461001);广西自然科学基金资助项目(0542048);广西民族大学基金资助重大科研项目

摘　　要：利用多项式根的反演关系,给出判定多项式根是否全部在单位圆内的判定定理。引入变形参数将多项式变形,并基于判定定理,给出求变形参数最小值的人工鱼群算法,即求多项式根最大模的人工鱼群算法,使变形多项式根全部在单位圆内。算例表明该算法收敛速度快,求解精度高。The theorem used to judge whether all roots of a polynomial are in unit circle is put forward. To transform the polynomial by the transforming parameter, and Artificial Fish School Algorithm（AFSA） for finding the minimum value of the transforming parameter which makes all the roots of the polynomial in unit circle based on the judging theorem is given. It is Artificial Fish School Algorithm for finding the largest module of roots of polynomial. Several computer simulation results show that using this algorithm to find the largest module of roots of polynomial is more efficient and feasible, and the convergent speed and the accuracy of result is higher.

关 键 词：多项式 根最大模 单位圆 判定定理 人工鱼群算法 

分 类 号：TP312[自动化与计算机技术—计算机软件与理论]