A convergence rate result for a steepest descent method and a minimal error method for the solution of nonlinear ill-posed problems (Q1891946)

The paper is devoted to the study of the convergence of a steepest descent method as well as the minimal error method applied to a nonlinear operator equation of the form \(F(x) = y\) for which the solution (which need not be unique) does not depend continuously on the right-hand side data \(y\). Assuming \(F\) is Lipschitz continuously differentiable and that certain additional conditions are satisfied, a convergence rate result is obtained in the noise free case. Finally, these conditions are illustrated for a parameter estimation problem.