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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.
Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates
(Springer, 2020) Kanagaraj, K.; Reddy, G.D.; George, S.
Fractional Tikhonov regularization (FTR) method was studied in the last few years for approximately solving ill-posed problems. In this study we consider the Schock-type discrepancy principle for choosing the regularization parameter in FTR and obtained the order optimal convergence rate. Numerical examples are provided in this study. © 2019, Korean Society for Informatics and Computational Applied Mathematics.