An optimal eighth-order derivative-free family of Potra-Pták's method
type: Item
instance of: scholarly article
title: An optimal eighth-order derivative-free family of Potra-Pták's method
zbMATH Open document ID: 1461.65078
author: Munish Kansal
author: Saurabh Bhatia
author: V. Kanwar
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: In this paper, we present a new three-step derivative-free family based on Potra-Pták's method for solving nonlinear equations numerically. In terms of computational cost, each member of the proposed family requires only four functional evaluations per full iteration to achieve optimal eighth-order convergence. Further, computational results demonstrate that the proposed methods are highly efficient as compared with many well-known methods.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 7042253
zbMATH Keywords: Steffensen-type methods
zbMATH Keywords: Kung-Traub conjecture
zbMATH Keywords: optimal order of convergence
zbMATH Keywords: efficiency index
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a8020309
OpenAlex ID: W1603497002
cites work: Q5326192
cites work: Optimal Order of One-Point and Multipoint Iteration
cites work: Q5723445
cites work: Q3343091
cites work: Q5732060
cites work: Q4752897
cites work: Derivative free two-point methods with and without memory for solving nonlinear equations
cites work: A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem
cites work: An optimized derivative-free form of the Potra-Pták method
cites work: Optimal Steffensen-type methods with eighth order of convergence
cites work: An optimal Steffensen-type family for solving nonlinear equations
cites work: On a bi-parametric class of optimal eighth-order derivative-free methods
DOI: 10.3390/A8020309
description: scientific article; zbMATH DE number 7042253