Regularization of linear and nonlinear ill-posed problems by mollification
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In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed equation T(f) =g where T can be nonlinear. The regularized solutions we define extend the work of Bonnefond and Maréchal <cit.>, and trace their origins in the variational formulation of mollification, which to the best of our knowledge, was first introduced by Lannes et al. <cit.>. In addition to consistency results, for the first time, we provide some convergence rates for a mollification method defined through a variational formulation.
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