𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Three-step iterative methods with eighth-order convergence for solving nonlinear equations

✍ Scribed by Weihong Bi; Hongmin Ren; Qingbiao Wu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
516 KB
Volume
225
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

A family of eighth-order iterative methods for the solution of nonlinear equations is presented. The new family of eighth-order methods is based on King's fourth-order methods and the family of sixth-order iteration methods developed by Chun et al. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2 n-1 . Thus we provide a new example which agrees with the conjecture of Kung-Traub for n = 4. Numerical comparisons are made to show the performance of the presented methods.

πŸ“œ SIMILAR VOLUMES

Three-step iterative methods with optima
Three-step iterative methods with optimal eighth-order convergence
✍ Alicia Cordero; Juan R. Torregrosa; MarΓ­a P. Vassileva πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 206 KB

order a b s t r a c t In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, s

New eighth-order iterative methods for s
New eighth-order iterative methods for solving nonlinear equations
✍ Xia Wang; Liping Liu πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 310 KB

## a b s t r a c t In this paper, three new families of eighth-order iterative methods for solving simple roots of nonlinear equations are developed by using weight function methods. Per iteration these iterative methods require three evaluations of the function and one evaluation of the first der

Alternative convergence criteria for ite
Alternative convergence criteria for iterative methods of solving nonlinear equations
✍ Hamilton A. Chase πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 877 KB

x,,, -J, m = 1, 2, 3 . . be an iteration method for solving the nonlinear problem F(X) = 0, where F(X) and its derivatives possess all of the properties required by T(x,,,). Then ifit can be established thatfor the problem at hand jlF(~,+ 1)i/ < &,, llF(x& V m > M,, (M, < co) and 0 < &,, < 1, dejini

A class of iterative methods with third-
A class of iterative methods with third-order convergence to solve nonlinear equations
✍ M. Γ‡etin KoΓ§ak πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 223 KB

Algebraic and differential equations generally co-build mathematical models. Either lack or intractability of their analytical solution often forces workers to resort to an iterative method and face the likely challenges of slow convergence, non-convergence or even divergence. This manuscript presen

A uniparametric family of three-step eig
A uniparametric family of three-step eighth-order multipoint iterative methods for simple roots
✍ Young Hee Geum; Young Ik Kim πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 245 KB

A uniparametric family of three-step eighth-order multipoint iterative methods requiring only a first derivative are proposed in this paper to find simple roots of nonlinear equations. Development and convergence analysis on the proposed methods is described along with numerical experiments includin