A Family of Newton Type Iterative Methods for Solving Nonlinear Equations
AbstractIn this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2n requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung and Traub’s conjecture (1974). Its error equations and asymptotic convergence constants are obtained. The n-point iterative methods with memory are obtained by using a self-accelerating parameter, which achieve much faster convergence than the corresponding n-point methods without memory. The increase of convergence order is attained without any additional calculations so that the n-point Newton type iterative methods with memory possess a very high computational efficiency. Numerical examples are demonstrated to confirm theoretical results. View Full-Text
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Wang, X.; Qin, Y.; Qian, W.; Zhang, S.; Fan, X. A Family of Newton Type Iterative Methods for Solving Nonlinear Equations. Algorithms 2015, 8, 786-798.
Wang X, Qin Y, Qian W, Zhang S, Fan X. A Family of Newton Type Iterative Methods for Solving Nonlinear Equations. Algorithms. 2015; 8(3):786-798.Chicago/Turabian Style
Wang, Xiaofeng; Qin, Yuping; Qian, Weiyi; Zhang, Sheng; Fan, Xiaodong. 2015. "A Family of Newton Type Iterative Methods for Solving Nonlinear Equations." Algorithms 8, no. 3: 786-798.