【摘要】 本文讨论了在无重根情况下,利用改进的Newton迭代法对一种同时求多项式零点的并行迭代法进行加速,得到了一种新的加速迭代法。首先证明了该方法是收敛的,并且理论证明出收敛阶至少是5阶;其次,分析了该方法的计算效率;最后通过实际的数值算例表明:计算收敛阶和定理结论是一致的,且本算法具有较高的计算效率。更多还原

【Abstract】 A parallel iteration method for simultaneously determining all roots of a polynomial equa- tion is proposed.By means of the modified Newton’s method,a new acceleration method is obtained. The method is proved to convergences to order 5 at least and its computing efficiency is analyzed. Numerical experiments show that the numerical order of convergence matches with the theorem’s con- clusion and the new method is more effective.更多还原