A class of Newton's methods with third-order convergence

作者：Zhou Xiaojian^*

来源：Applied Mathematics Letters, 2007, 20(9): 1026-1030.

DOI：10.1016/j.aml.2006.09.010

• variants of Newton's method
• simple roots
• power mean
• cubic convergence
• generalization

In this work, a class of iterative Newton's methods, known as power mean Newton's methods, is proposed. Some known results can be regarded as particular cases. It is shown that the order of convergence of the proposed methods is 3. Numerical results are given to verify the theory and demonstrate the performance.

• 出版日期2007-9
• 单位南通大学