Simply constructed family of a Ostrowski's method with optimal order of convergence

Authors:
V. Kanwar;Ramandeep Behl;Kapil K. Sharma
Affiliations:
University Institute of Engineering and Technology, Panjab University, Chandigarh- 160 014, India;Department of Mathematics, Panjab University, Chandigarh-160 014, India;Department of Mathematics, Panjab University, Chandigarh-160 014, India
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 4
Cited 0

Optimal Order of One-Point and Multipoint Iteration

Journal of the ACM (JACM)
A new continuation Newton-like method and its deformation

Applied Mathematics and Computation
A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function

Computers & Mathematics with Applications
Accurate fourteenth-order methods for solving nonlinear equations

Numerical Algorithms

Quantified Score

Hi-index	0.10

Visualization

Abstract

In this paper, we propose a simple modification over Chun's method for constructing iterative methods with at least cubic convergence [5]. Using iteration formulas of order two, we now obtain several new interesting families of cubically or quartically convergent iterative methods. The fourth-order family of Ostrowski's method is the main finding of the present work. Per iteration, this family of Ostrowski's method requires two evaluations of the function and one evaluation of its first-order derivative. Therefore, the efficiency index of this Ostrowski's family is E=43~1.587, which is better than those of most third-order iterative methods E=33~1.442 and Newton's method E=2~1.414. The performance of Ostrowski's family is compared with its closest competitors, namely Ostrowski's method, Jarratt's method and King's family in a series of numerical experiments.