Regularization of linear and nonlinear ill-posed problems by mollification

2020/03/17 by Walter Cédric Simo Tao Lee, Lee, Walter Cedric Simo Tao
Mathematics · Engineering · #Numerical methods in inverse problems #Statistical and numerical algorithms #Microwave Imaging and Scattering Analysis

paper · pdf · doi:10.48550/arxiv.2003.07913

Abstract

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 \citexapi, and trace their origins in the variational formulation of mollification, which to the best of our knowledge, was first introduced by Lannes et al. \citelannes. In addition to consistency results, for the first time, we provide some convergence rates for a mollification method defined through a variational formulation.

Citations

• A Global Uniqueness Theorem for an Inverse Boundary Value Problem

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