一种求解多项式方程复数根的新方法

A new method for solving complex roots of polynomial equations

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.

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 convergence,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 mechanism of genetic algorithm and the basic idea of parallel computing,it has strong adaptability and global convergence.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 number and the plural is shown in this paper,which shows that the genetic algorithm combined with the parallel computing has good applicability in solving the complex root of polynomial equation.