Regularization of autoconvolution and other ill-posed quadratic equations by decomposition (Q2877849)

In this clearly written paper, the author discusses the regularization of quadratic equations, which arise in a number of contexts, e.g., autoconvolution, and proposes a decomposition approach as follows. First, the forward operator is split into a bounded linear operator and a strong quadratic isometry (Theorem 3.1), then the ill-posed but linear operator equation is solved using classical Tikhonov regularization, and finally the unknown of interest is recovered by solving a well-posed quadratic equation. The influence of discretization is also briefly discussed. One advantage of the approach is that it avoids computing the derivative of the nonlinear forward map and thus relaxes the differentiability requirement.