Abstract: 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.

Key words: polynomial, the largest module of roots, unit circle, judging theorem, Artificial Fish School Algorithm(AFSA)

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。

关键词: 多项式, 根最大模, 单位圆, 判定定理, 人工鱼群算法

CLC Number: 

• TP312