Journal ArticleDOI
A Family of Fourth Order Methods for Nonlinear Equations
TLDR
A family of fourth order iterative methods for finding simple zeros of nonlinear functions is presented in this paper, which require evaluation of the function and its derivative at the starting point of the algorithm.Abstract:
A family of fourth order iterative methods for finding simple zeros of nonlinear functions is displayed. The methods require evaluation of the function and its derivative at the starting point of e...read more
Citations
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Journal ArticleDOI
Optimal Order of One-Point and Multipoint Iteration
TL;DR: It is proved that the optimal order of one general class of multipoint iterations is 2 and that an upper bound on the order of a multipoint iteration based on n evaluations of ƒ (no derivatives) is 2.
Journal ArticleDOI
Graphic and numerical comparison between iterative methods
TL;DR: A simplified version of the Newton-Raphson method was proposed by Raphson in 1690 as mentioned in this paper, which is also known as the Newman-Rodriguez method.
Journal ArticleDOI
Basin attractors for various methods
TL;DR: It can be seen that not all higher order methods were created equal, namely the basin of attraction of the method and its dependence on the order.
Review of some iterative root-finding methods from a dynamical point of view
TL;DR: In this article, the root-finding iterative methods of Chebyshev, Stirling, and Steffensen were studied from a dynamical point of view applied to complex polynomials.
Journal ArticleDOI
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
TL;DR: In this paper, a family of 8-order iterative methods for nonlinear equations is presented, based on King's fourth-order methods and the family of 6-order iteration methods developed by Chun et al. Each iteration requires three evaluations of the function and one derivative.
References
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Journal ArticleDOI
Some efficient fourth order multipoint methods for solving equations
TL;DR: In this paper, a simple and efficient fourth order multipoint iterative method for solving equations is presented, and comparisons of computational efficiency are made with other well known techniques and a numerical example is given.