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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 yδ with ‖yδ − y‖ ≤ δ. In this method, the iterative sequence {xk} is defined successively by xk+1 = x δ k − (αkI +F (xk)F (xk)) ( F (xk) ∗(F (xk)− y) +αk(xk − x0) ) , where x0 := x0 is(More)
In this paper, we consider the finite-dimensional approximations of Tikhonov regularization 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)
In this paper, we consider the finite-dimensional approximations of Tikhonov regularization 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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