Abstract
In this paper, we deal with nonlinear ill-posed operator equations involving a monotone operator in the setting of Hilbert scales. Our convergence analysis of the proposed derivative-free method is based on the simple property of the norm of a self-adjoint operator. Using a general Hölder-type source condition, we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. Finally, we applied the proposed method to the parameter identification problem in an elliptic PDE in the setting of Hilbert scales and compare the results with the corresponding method in Hilbert space.
Funding statement: The work of Santhosh George is supported by the Core Research Grant by SERB, Department of Science and Technology, Government of India, EMR/2017/001594. K. Kanagaraj would like to thank National Institute of Technology Karnataka, India, for the financial support.
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