Two new families of iterative methods for solving nonlinear equations

Kalyanasundaram M ； J. Jayakumar

《Tamsui Oxford Journal of Information and Mathematical Sciences》 31卷1期 (2017/02) Pp. 25-38

摘要

In this paper, we have presented a family of fourth order iterative method and another family of sixth order iterative method without memory based on power mean using weight functions. The family of fourth order methods given here is optimal in the sense of Kung-Traub hypothesis. In terms of computational point of view, our first method require three evaluations (one function and two first derivatives) per iteration to get fourth order and the second method require four evaluations (two functions and two derivatives) per iteration to get sixth order. Hence, these methods have high efficiency indices 1.5874 and 1.5651 respectively. Few existing methods can be regarded as particular cases of our family of methods. Some numerical examples are tested to know the performance of the new methods which verifies the theoretical results.

關鍵字

Non-linear equation ； Multi-point iteration ； Optimal order ； Kung-Traub conjecture ； Power mean