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Sixteenth-order method for nonlinear equations |
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| Authors: | Xiaowu Li Chunlai Mu Chan Wang |
| Institution: | a College of Mathematics and Physics, Chongqing University, Chongqing 400044, PR China b School of Mathematical Sciences, Peking University, Beijing 100871, PR China c China Economics and Management Academy, Central University of Finance and Economics, Beijing 100081, PR China |
| Abstract: | Modification of Newton’s method with higher-order convergence is presented. The modification of Newton’s method is based on King’s fourth-order method. The new method requires three-step per iteration. Analysis of convergence demonstrates that the order of convergence is 16. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton’s method and other methods. |
| Keywords: | Nonlinear equations Iterative methods Newton&rsquo s method Order of convergence |
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