On efficient two-parameter methods for solving nonlinear equations

Authors:
Jovana Džunić
Affiliations:
Faculty of Electronic Engineering, Department of Mathematics, University of Niš, Niš, Serbia 18000
Venue:
Numerical Algorithms
Year:
2013

Citing 5
Cited 1

Optimal Order of One-Point and Multipoint Iteration

Journal of the ACM (JACM)
Principles for Testing Polynomial Zerofinding Programs

ACM Transactions on Mathematical Software (TOMS)
Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”

SIAM Journal on Numerical Analysis
On generalized multipoint root-solvers with memory

Journal of Computational and Applied Mathematics
Iterative methods for solving nonlinear equations with finitely many roots in an interval

Journal of Computational and Applied Mathematics

On generalized biparametric multipoint root finding methods with memory

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Derivative free methods for solving nonlinear equations of Steffensen's type are presented. Using two self-correcting parameters, calculated by Newton's interpolatory polynomials of second and third degree, the order of convergence is increased from 2 to 3.56. This method is used as a corrector for a family of biparametric two-step derivative free methods with and without memory with the accelerated convergence rate up to order 7. Significant acceleration of convergence is attained without any additional function calculations, which provides very high computational efficiency of the proposed methods. Another advantage is a convenient fact that the proposed methods do not use derivatives. Numerical examples are given to demonstrate excellent convergence behavior of the proposed methods and good coincidence with theoretical results.