We report on a new iterative method for regularizing a nonlinear operator equation in Hilbert spaces. The proposed algorithm is a combination of Tikhonov regularization and a fixed point algorithm for the minimization of the Tikhonov functional. Under the assumptions that the operator F is twice continuous Fréchet-differentiable with Lipschitz-continuous first derivative and that the solution of the equation F (x) = y fulfills a smoothness condition we will give a convergence rate result. Numerical results with data from Single Photon Emission Computed Tomography (SPECT) show the rapid convergence of the proposed algorithms.
Editor-in-Chief: Kabanikhin, Sergey I.
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On the use of fixed point iterations for the regularization of nonlinear ill-posed problems
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∗University of Bremen, Germany. E-mail: ramlau@math.uni-bremen.de
Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 13, Issue 2, Pages 175–200, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/1569394053978498,
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