多项多实根的一种求解方法

通过将多项式简单地分解为正负两个部分，提出了求解多项式最大正极和最小正根的迭代算法，在此基础上，利用因式分解定理得到了其所有正根的计算方法，证明了它的收敛性，并估计了收敛速度。在确保收敛的情况下，本文又引入一个辅助函数对两种方法进行了修正，修正后的算法使得计算量大为减少，而其收敛速度却没有受到影响。

A Method for Solving the Real Roots of a Polynomial

Through dividing simply a polynomial into two positive and negative parts,an iterative method for solving its maximal and minimal positive roots is given in this paper. Based on the method, a method for solving the real roots of a polynomial is reached by factorization theorem, its convergence is proved, and its convergent order is estimated. In order to decrease the complexity of the method, an auxiliary function is introduced, so that a revised method is obtained, but its convergence and order are not changed.