Convergence radius of the modified Newton method for multiple zeros under Hölder continuous derivative |
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| Authors: | Hongmin Ren Ioannis K Argyros |
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| Institution: | a Department of Information and Electronics, Hangzhou Radio and TV University, Hangzhou 310012, Zhejiang, PR China
b Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA |
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| Abstract: | In recent years, a lot of iterative methods for finding multiple zeros of nonlinear equations have been presented and analyzed. However, almost all these studies give no information for the convergence radius of the corresponding method. In this paper, we give an estimate of the convergence radius of the well-known modified Newton’s method for multiple zeros, when the involved function satisfies a Hölder and center-Hölder continuity condition. |
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| Keywords: | Nonlinear equations Zero-finding The modified Newton method Multiple zeros Convergence radius Hö lder condition Divided differences |
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