一类五阶牛顿变形方法及其加速

A Class of Fifth-Order Convergence Variants of Newton's Method and Its Acceleration

结合经典牛顿法与中点牛顿法,提出了一类求解非线性方程的五阶收敛迭代算法,并建立了该牛顿变形方法的加速公式.数值试验结果表明:相对于经典牛顿法、中点牛顿法、几何平均牛顿法、调和平均牛顿法和Simpson牛顿法等几种已有的牛顿改进格式,此类新型牛顿变形方法的收敛速度更快,精度更高.

Based on the classical Newton＇s method and the midpoint Newton＇s method,the paper presented a new fifth-order convergent iterative algorithm and its acceleration formula for nonlinear equations.Results of the numerical experiments show that the proposed algorithm is more accurate and efficient than the classical Newton＇s method and several existing Newton improving formats,such as Midpoint Newton＇s method,Geometrical mean Newton＇s method,Harmonic mean Newton＇s method and Simpson Newton＇s method.