A derivative-free iterative method for nonlinear ill-posed equations with monotone operators
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Date
2017
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Journal ISSN
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Publisher
Walter de Gruyter GmbH info@degruyter.com
Abstract
Recently, Semenova [12] considered a derivative free iterative method for nonlinear ill-posed operator equations with a monotone operator. In this paper, a modified form of Semenova's method is considered providing simple convergence analysis under more realistic nonlinearity assumptions. The paper also provides a stopping rule for the iteration based on an a priori choice of the regularization parameter and also under the adaptive procedure considered by Pereverzev and Schock [11]. © 2017 Walter de Gruyter GmbH, Berlin/Boston.
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Keywords
Control nonlinearities, Mathematical operators, Nonlinear equations, Adaptive methods, Convergence analysis, Derivative-free methods, Ill-posed operator equation, Lavrentiev regularizations, Monotone operators, Nonlinear ill-posed equations, Regularization parameters, Iterative methods
Citation
Journal of Inverse and Ill-Posed Problems, 2017, 25, 5, pp. 543-551