TIGRA
TIGRA -- an iterative algorithm for regularizing nonlinear ill-posed problems. A sophisticated numerical analysis of a combination of Tikhonov regularization and the gradient method for solving nonlinear ill-posed problems is presented. The TIGRA (Tikhonov-gradient method) algorithm proposed uses steepest descent iterations in an inner loop for approximating the Tikhonov regularized solutions with a fixed regularization parameter and a parameter iteration for satisfying a discrepancy criterion in an outer loop. The method with given convergence rate results works in a Hilbert space setting whenever the nonlinear forward operator is twice continuous Fréchet differentiable with a Lipschitz-continuous first derivative and obvious source conditions are fulfilled. For applying the method the forward operator must be defined on the whole Hilbert space, which seems to be the essential restriction of the given approach. Numerical results are presented for an inverse problem occurring in single-photon-emission computed tomography, where the assumptions of the paper are satisfied.
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References in zbMATH (referenced in 37 articles , 1 standard article )
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- Sabari, M.; George, Santhosh: Modified minimal error method for nonlinear ill-posed problems (2018)
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- Argyros, Ioannis K.; George, Santhosh; Jidesh, P.: Inverse free iterative methods for nonlinear ill-posed operator equations (2014)
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- Brandt, C.; Niebsch, J.; Ramlau, R.; Maass, P.: Modeling the influence of unbalances for ultra-precision cutting processes (2011)
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- Beilina, L.; Klibanov, M. V.; Kokurin, M. Yu.: Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem (2010)
- Kokurin, M. Yu.: The global search in the Tikhonov scheme (2010)
- Kokurin, M. Yu.: Convexity of the Tikhonov functional and iteratively regularized methods for solving irregular nonlinear operator equations (2010)