A Newton-type method for nonlinear ill-posed problems with A-smooth regularization
In this paper we present a regularized Newton-type method for ill-posed problems, by using the A-smooth regularization to solve the linearized ill-posed equations. For noisy data a proper a posteriori stopping rule is used that yields convergence of the Newton iteration to a solution, as the noise level goes to zero, under certain smoothness conditions on the nonlinear operator. Some appropriate assumptions on the closedness and smoothness of the starting value and the solution are shown to lead to optimal convergence rates.
nonlinear ill-posed problems, A-smooth regularization, a posteriori stopping rule, convergence and convergence rates.
殷萍、贺国强、孟泽红
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Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China
nonlinear ill-posed problems, A-smooth regularization, a posteriori stopping rule, convergence and convergence rates.