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Convergence rate results for steepest descent type method for nonlinear ill-posed equations
(Elsevier Inc. usjcs@elsevier.com, 2017) George, S.; Sabari, M.
Convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill-posed operator equation have been proved with noisy data. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide a convergence rate results for these methods with noisy data. The result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method. We present an academic example which satisfies the assumptions of this paper. © 2016 Elsevier Inc.
Modified Minimal Error Method for Nonlinear Ill-Posed Problems
(Walter de Gruyter GmbH cmam@cmam.info, 2018) Sabari, M.; George, S.
An error estimate for the minimal error method for nonlinear ill-posed problems under general a Hölder-type source condition is not known. We consider a modified minimal error method for nonlinear ill-posed problems. Using a Hölder-type source condition, we obtain an optimal order error estimate. We also consider the modified minimal error method with noisy data and provide an error estimate. © 2018 Walter de Gruyter GmbH, Berlin/Boston.