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A cubically convergent Newton-type method under weak conditions |
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| Authors: | Liang Fang Guoping He Zhongyong Hu |
| Institution: | aDepartment of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, China;bDepartment of Mathematics and System Science, Tai Shan University, 271021, Tai’an, China;cCollege of Information Science and Engineering, Shandong University of Science and Technology, 266510, Qingdao, China |
| Abstract: | Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f′(x)=0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative. Analysis of convergence demonstrates that the new method is cubically convergent. Some numerical examples illustrate that the algorithm is more efficient and performs better than classical Newton's method. |
| Keywords: | Newton's method Nonlinear equations Iterative method Third-order convergence |
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