A Newton-type method for a transmission problem in inverse scattering

The iteratively regularized Gauss-Newton method is applied to solve an inverse transmission problem for the Helmholtz equation, which is known to be nonlinear and severely ill-posed. We first present a simplified proof of the characterization of the Frechet derivative. Based on this result, we describe an efficient numerical implementation including an error analysis. Finally, we investigate the speed of convergence of the Newton iteration both for exact and for noisy data.