基于多项式根最大模求解的二分搜索算法

Binary Search Algorithm Based on Solving the Maximum Module of Roots of Polynomial

传统多项式根最大模求解算法的求解效率低、计算复杂。针对该问题,提出一种基于多项式根的最大模求解的二分搜索算法。该算法通过选取模的上下界确定初始搜索区间,利用判定定理判断多项式的根与单位圆的关系,从而求得多项式任意精度的最大模。仿真结果表明,该算法收敛速度快、求解精度高。

Classic algorithm is slow and complex for solving the maximum module of the roots of polynomials. Aiming at these problems, this paper presents a binary search algorithm based on solving the maximum module of roots of polynomial. In the algorithm, the initialized search interval is selected by the maximum module bounds, and the theorem is used to decide whether all roots of a polynomial are in unit circle. It can obtain an arbitrary precision maximum module. Simulation results show that the algorithm has fast convergence rate and high precision.