.png){kind=icon}
.png){kind=icon}
Return
Some efficient derivative free methods with memory for solving nonlinear equations
.png){kind=icon}
PRE
AI
DOI：10.1016/j.amc.2012.06.062.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Based on the family of three-point derivative free methods without memory of eighth order convergence proposed by Dzunic et al. [J. Dzunic, M. S. Petkovic, L. D. Petkovic, Three-point methods with and without memory for solving nonlinear equations, Appl. Math. Comput. 218 (2012) 4917-4927], we present three methods with memory by suitable variation of a free parameter in each iterative step. This free parameter is calculated using Newton's interpolatory polynomial of the third degree in two ways and Newton's interpolatory polynomial of the fourth degree. Consequently, the R-order of convergence is increased from 8 to 11+root 137/2 approximate to 11.352, 6 + 4 root 2 approximate to 11.657 and 12. The increase in the convergence order is achieved without any additional function evaluations and therefore, the proposed methods possess a very high computational efficiency. Numerical examples are presented and the performance is compared with the existing three-point methods with and without memory of the basic family. Moreover, theoretical order of convergence is verified on the examples. (C) 2012 Elsevier Inc. All rights reserved.
Keywords:
Nonlinear equations
Multipoint iterative methods
Methods with memory
Derivative free methods
Acceleration of convergence
R-order of convergence
Computational efficiency
Journal
IF:
3.4
Papers:
2.3W
Citations:
3.3W