Finite dimensional realization of the FTR method with Raus and Gfrerer type discrepancy principle

Abstract

It is known that the standard Tikhonov regularization methods oversmoothen the solution x^ of the ill-posed equation T(x) = y, so the computed approximate solution lacks many inherent details that are expected in the desired solution. To rectify this problem, Fractional Tikhonov Regularization (FTR) method have been introduced. Kanagaraj et al. (J Appl Math Comput 63(1):87–105, 2020), studied FTR method for solving ill-posed problems. Techniques are developed to study the Finite Dimensional FTR (FDFTR) method. We also study Raus and Gfrerer type discrepancy principle for FDFTR method and compare the numerical results with other discrepancy principles of the same type. © 2023, The Author(s), under exclusive licence to Springer-Verlag Italia S.r.l., part of Springer Nature.