Newton-Tikhonov regularization of ill-posed Hammerstein operator equation

摘要

In this paper we report on a new iterative method for regularizing a nonlinear Hammerstein operator equation in Hilbert spaces. The proposed Newton-Tikhonov method is a combination of Tikhonov regularization and a Newton's iteration. Under the assumptions that the operator F is continuous Fréchet differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a smoothness condition, we will give a convergence rate result.