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Inexact-Newton method for solving operator equations in infinite-dimensional spaces |
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| Authors: | Jing Liu Yan Gao |
| Institution: | 1. School of Management, University of Shanghai for Science and Technology, Jungong Road, 191 box, 200093, Shanghai, P.R. China 2. Department of Mathematics, Harbin Normal University, 150080, Harbin, P.R. China 3. School of Management, University of Shanghai for Science and Technology, Jungong Road, 200093, Shanghai, P.R. China |
| Abstract: | In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces. |
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