Sourcewise representation of solutions to nonlinear operator equations in a Banach space and convergence rate estimates for a regularized Newton’s method

Abstract

Abstract - We present a class of iterative methods for solving nonlinear ill-posed operator equations with differentiable operators in a Banach space. The methods are based on regularization of the linearized equation by using an appropriate regularization scheme at each iteration. We establish that the iterations converge locally with power rate provided that the solution admits of a sourcewise representation. We also prove that the condition of sourcewise representability is very close to a necessary condition for this kind of estimates.