A Novel n-Point Newton-Type Root-Finding Method of High Computational Efficiency

• Published in: Mathematics (Basel) Vol. 10; no. 7; p. 1144
• Main Author: Wang, Xiaofeng
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2022
• Subjects: Approximation; Attraction; Basins; Computational efficiency; Computing time; Efficiency; Interpolation; Iterative methods; Mathematics; Methods; nonlinear equation; Nonlinear equations; Numerical methods; optimal convergence order; Stability

A novel Newton-type n-point iterative method with memory is proposed for solving nonlinear equations, which is constructed by the Hermite interpolation. The proposed iterative method with memory reaches the order (2n+2n−1−1+22n+1+22n−2+2n+1)/2 by using n variable parameters. The computational effici...