非线性方程重根的三阶迭代方法

Third Order Convergence Method for Finding Multiple Roots of Nonlinear Equations

为提高求解非线性方程的收敛速度和计算效率,以牛顿法为基础提出一种求解非线性方程重根的迭代方法,该方法以重数已知为前提,迭代格式根据重数为奇数和偶数两种情形分别给出,两种迭代格式每步迭代都只需计算三个函数值(包含一阶导数值)且完全摆脱了二阶导数值的计算,其收敛效果皆可达到三阶.算例实验结果验证了该迭代方法的有效性.他丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值.

In order to improve the convergence speed and computational efficiency of the method for solving nonlinear equations, a third order method with known multiplicity for finding multiple roots of nonlinear equations is developed in this paper. Two iterative algorithms are given according to the even or odd quality of the multiplicity respectively. The method is based on the modified Newton＇ s method and it requires three evaluations of the func- tions （ include the evaluations of the first order derivative） free from the evaluations of second derivatives totally. It enriches the methods of solving nonlinear equations and has great significance in both theory and application.