A Convergence Analysis of the Iterated Lavrentiev Regularization Method under a Lipschitz Condition. (25th January 2022) - Mahale, Pallavi; Singh, Ankit
Abstract: Mahale and Nair (2009) considered a iterated Lavrentive regularization method for obtaining stable approximate solution of nonlinear ill-posed operator equation F ( x ) = y, where F : D ( F ) ⊂ X → X is a nonlinear monotone operator on Hilbert space X . In this paper, we do convergence analysis of the method under the weaker non-linearity condition than the one considered by Mahale and Nair. We obtain convergence and rate of convergence results for the method merely under Lipschitz's condition. At the end of the paper, we give a numerical example to demonstrate our algorithm.