An Accelerated Iterative Method with Third-Order Convergence

Abstract:

We present a new modified Newton's method with third-order convergence and compare it with the Jarratt method, which is of fourth-order. Based on this new method, we obtain a family of Newton-type methods, which converge cubically. Numerical examples show that the presented method can compete with Newton's method and other known third-order modifications of Newton's method.

• Periodical: Applied Mechanics and Materials (Volumes 220-223)
• Pages: 2658-2661
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.220-223.2658
• Online since: November 2012
• Authors: Zhong Yong Hu, Liang Fang, Lian Zhong Li
• Keywords: Acceleration, Newton Method, Third-Order Convergence

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