一种求解多项式方程复数根的新方法

摘要

Solving of polynomial equations is a common computing problem in engineering design .Among the existing solutions , the Splitting Factor Method has the problems of slow convergence speed and no conver-gence , which leads to some limitations of the application of polynomial equations .Therefore , this paper proposes a new method to solve the defect of the Splitting Factor Method .In this method , combining the iterative mecha-nism of genetic algorithm and the basic idea of parallel computing , it has strong adaptability and global conver-gence.Especially in the solution of complex roots , this advantage is more obvious .Compared with the Splitting Factor Methods, this method not only avoids complex operation , but also has lower algorithm complexity and higher computational precision .For example , in numerical experiments , the relationship between the real num-ber and the plural is shown in this paper , which shows that the genetic algorithm combined with the parallel com-puting has good applicability in solving the complex root of polynomial equation .%多项式方程的求解是许多工程设计中的比较常见的计算问题.在现有的求解方法中,常用的劈因子方法存在收敛速度慢和不收敛的情况,从而导致多项式方程的应用受到一定程度的局限.因此,针对这种劈因子方法的缺陷,提出了一种新的求解方法.在该方法中,由于采用了遗传算法的迭代机制和并行计算的基本思想,从而具有较强的自适应性和全局的收敛性.特别是在复数根的求解方面,这种优势更加明显.相对于劈因子方法来说,该方法不仅避免了复数运算,还具有较低的算法复杂度和较高的计算精度.例如,在数值实验中,所展示的实数部与虚数部的关系,从而表明遗传算法和并行计算思想在多项式方程复数根求解过程中,具有良好的应用性.