A cubically convergent Newton-type method under weak conditions

作者：Fang, Liang^*; He, Guoping; Hu, Zhongyong

来源：Journal of Computational and Applied Mathematics, 2008, 220(1-2): 409-412.

DOI：10.1016/j.cam.2007.08.013

• Newton's method
• nonlinear equations
• iterative method
• third-order convergence

Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f'(x) = 0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton's method.

• 出版日期2008-10-15
• 单位上海交通大学; 山东科技大学; 泰山学院