单变元多项式方程的高效区间牛顿算法

An Efficient Interval Newton Algorithm for Univariate Polynomial Equation

为了解决当前存在的区间运算复杂性高、普通区间迭代程序运算量大、花费机器时间长等问题,提高区间迭代的运算效率,针对单变元多项式方程的求解展示了一个高效的区间Newton迭代算法。该算法利用1维问题多维化的思想加快迭代的收敛速度,改进了多维化过程中出现的性能拖累,极大地提高了算法在实际应用中的执行效率。算法已经被实现为M ap le程序,实验数据表明,与现有的算法相比,这个算法的迭代次数和运行时间都大幅减少,充分显示了它的高效性。

An efficient interval Newton algorithm for univariate polynomial equation was proposed.This algorithm reduced greatly the number of iterations and computations based on Hansen＇s method for univariate polynomial equation.The algorithm was implemented as a Maple program.Compared with the existing algorithm,this algorithm was dramatically fast in some cases.A large number of polynomials generated randomly by Maple were tested and the performance was reported.