【摘要】 为了保证牛顿-拉夫森算法中迭代所采用的二阶导数矩阵的正定性,进一步改善算法的收敛速度和迭代精度,提出了两个方面的改进:一方面,对二阶导数矩阵作了修正以确保其成为正定矩阵,从而改善了收敛速度;另一方面,引入了一个修正因子对每次迭代的结果加以修正,来提高迭代精度。仿真结果表明,改进的牛顿-拉夫森算法所得到的结果精度更高,而且收敛速度也有所提高,也验证了改进方法的正确性和有效性。更多还原

【Abstract】 In order to ensure that the second differential matrix of Newton-Raphson algorithm used in every iterative step is always positive to improve convergence rate and iterative precision,two points are developed for improving Newton-Raphson algorithm: on the one hand,the second differential matrix is modified to become a positive matrix,which enhances its convergence rate;on the other hand,a revising factor is adopted to revise the iterative result,which advances its iterative precision.The simulation results dicided by using improved Newton-Raphson algorithm indicates that the precision of results is better and its convergence rate is faster.Therefor,the simulation results verify that the improved method is correct and effective.更多还原