On the use of fixed point iterations for the regularization of nonlinear ill-posed problems
نویسنده
چکیده
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. AMS Classification. 65J15, 65J20, 65J22, 44A12
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تاریخ انتشار 2004