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The iteratively regularized Gauss-Newton method is applied to compute the stable solutions to nonlinear ill-posed problems F (x) = y when the data y is given approximately by y δ with y δ − y ≤ δ. In this method, the iterative sequence {x δ k } is defined successively by x δ k+1 = x δ k − (α k I + F (x δ k) * F (x δ k)) −1 F (x δ k) * (F (x δ k) − y δ) + α(More)
In this paper, we consider the finite-dimensional approximations of Tikhonov regu-larization for nonlinear ill-posed problems with approximately given right-hand sides. We propose an a posteriori parameter choice strategy, which is a modified form of Morozov's discrepancy principle , to choose the regularization parameter. Under certain assumptions on the(More)
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