YANG Jing, HUANG Hai-yang, WANG Xia and et al. Some improvements of HN method with sixth-order covergence[J]. Journal of Light Industry, 2011, 26(2): 116-120. doi: 10.3969/j.issn.1004-1478.2011.02.029
Citation:
YANG Jing, HUANG Hai-yang, WANG Xia and et al. Some improvements of HN method with sixth-order covergence[J]. Journal of Light Industry, 2011, 26(2): 116-120.
doi:
10.3969/j.issn.1004-1478.2011.02.029
Some improvements of HN method with sixth-order covergence
-
Dept.of Mathe.and Infor.Sci., Zhengzhou Univ.of Light Ind., Zhengzhou 450002, China;
-
Suzhou No.9 Middle School of Anhui Province, Suzhou 234000, China
-
Received Date:
2011-02-23
Available Online:
2011-03-15
Fund Project:
Basic and Cutting-edge Technology Research Projrcts of He'nan Province(092300410045)The National Science Foundation of the Education Department of He'nan Province(2010A520045)
-
Abstract
Two families of sixth-order methods are developed by extending a third-order HN method (harmonic mean Newton's method) for finding the real roots of nonlinear equation in R.The convergence analysis is provided to establish their sixth-order of convergence.In terms of computational cost,they require evaluations of only two functions and two first derivatives per iteration.This implies that efficiency index of our methods are 1.565.Our methods are comparable with Newton's method,HN method and others,as we show in some examples.In the end,some improvements of AN method (arithmetic mean Newton's method) were given.
-
-
References
-
Proportional views
-
-
DownLoad: