2013/02/02 by Laila M Assas, Assas, Laila M, Fayyaz Ahmad +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1302.0419
openalex publication_date 2013/02/02 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this note, we present an eighth-order derivative-free family of iterative\nmethods for nonlinear equations. The proposed family shows optimal eight-order\nof convergence in the sense of the Kung and Traub conjecture cite5 and is\nbased on the Steffensen derivative approximation used in the Newton-method. As\na final step, having in mind computational purposes, a derivative-free\npolynomial base interpolation is used in order to get optimal order of\nconvergence with only four functional evaluations. Numerical esperiments and\nfew issues are discussed at the end of this note.\n