On Newton's method under Hölder continuous derivative |
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| Authors: | Huang Zhengda |
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| Institution: | Department of Mathematics, Xixi Campus, Zhejiang University, Tianmusan Road 34, Hangzhou 310028, PR China |
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| Abstract: | A Mysovskii-type theorem for Newton's method under (k,p)-Hölder continuous derivative is considered in this paper. For the application studied by others, the new condition is weaker than ones in the literature. Also we prove that the optimal convergent order is p+1 for 0<p<1. |
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| Keywords: | Newton's method Semilocal convergence Convergent order |
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