An improvement of Chebyshev-Halley methods free from second derivative

作者：Li, Dingfang^*; Liu, Ping; Kou, Jisheng

来源：Applied Mathematics and Computation, 2014, 235: 221-225.

DOI：10.1016/j.amc.2014.02.083

• Chebyshev-Halley method
• Newton method
• Non-linear equations
• Iterative method
• Root-finding

In this paper, a family of modified Chebyshev-Halley's methods free from second derivative is presented. Per iteration the new methods require three evaluations of the function and one of its first derivatives. A detailed convergence analysis of the new methods shows that the new methods are at least fifth-order convergent and especially, the modified super-Halley's method is sixth-order convergent. Numerical examples are given to illustrate the efficiency and performance of the new methods.

• 出版日期2014-5-25
• 单位湖北工程学院; 武汉大学