On the complexity of extending the convergence ball of Wang’s method for finding a zero of a derivative |
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Institution: | 1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, PR China;2. Shenzhen Key Laboratory of Advanced Machine Learning and Applications, College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, PR China;3. School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, PR China;4. Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung, Taiwan |
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Abstract: | Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study. |
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Keywords: | Wang’s method Convergence ball Error estimates Lipschitz continuity Center Lipschitz continuity |
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