Improved Chebyshev–Halley methods with sixth and eighth order convergence

Janak Raj Sharma

Applied Mathematics and Computation, 2015, vol. 256, issue C, 119-124

Abstract: We present a second derivative free family of modified Chebyshev–Halley methods with increasing order of convergence for solving nonlinear equations. The idea is based on the recent development by Li et al. (2014). Analysis of convergence shows that the family possesses at least sixth order of convergence. In a particular case even eighth order of convergence is achieved. Per iteration each method of the family requires four evaluations, namely three functions and one first derivative. That means, the eighth order method is optimal in the sense of Kung–Traub hypothesis. Numerical tests are performed, which confirm the theoretical results regarding order of convergence and efficiency of the new methods.

Keywords: Iterative methods; Chebyshev–Halley method; Newton method; Optimal order; Computational efficiency (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315000077
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:119-124

DOI: 10.1016/j.amc.2015.01.002

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().