两类求解非线性方程的高阶算法

Two Families of Higher Order Algorithms for Solving Nonlinear Equations

将加速技术与一些三阶方法相结合,提出了一类具有四阶收敛性的牛顿迭代改进方法;利用线性插值法与Homeier-Simpson Newton方法相结合,构造了一类五阶牛顿迭代改进方法;分析了新算法的收敛性,并给出了误差估计.通过数值算例,对新算法与已有算法的性能进行了比较,数值结果表明新方法是可行的.

In this paper,we propose a class of Newton improved methods with fourth-order convergence by combining the acceleration technique with some third-order methods,and construct a class of fifth order Newton improved methods by combining linear interpolation with the homeier-Simpson Newton method.The convergence of the new algorithms is ana-lyzed,and the error estimations are given.In addition,some examples are given to compare the performance of the new methods and the existing algorithms.The numerical results show that the new methods are feasible.