On the local convergence of inexact Newton-type methods under residual control-type conditions |
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Authors: | Hongmin Ren |
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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: | A local convergence analysis of inexact Newton-type methods using a new type of residual control was recently presented by C. Li and W. Shen. Here, we introduce the center-Hölder condition on the operator involved, and use it in combination with the Hölder condition to provide a new local convergence analysis with the following advantages: larger radius of convergence, and tighter error bounds on the distances involved. These results are obtained under the same hypotheses and computational cost. Numerical examples further validating the theoretical results are also provided in this study. |
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Keywords: | 65H10 65H15 65F18 65G99 47H17 49M15 |
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