On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems
On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems
The iteratively regularized Gauss-Newton method is applied to compute the stable solutions to nonlinear ill-posed problems $F(x)=y$ when the data $y$ is given approximately by $y^\delta$ with $\|y^\delta -y\|\le \delta$. In this method, the iterative sequence $\{x_k^\delta \}$ is defined successively by \[ x_{k+1}^\delta =x_k^\delta -(\alpha _k I+F'(x_k^\delta )^*F'(x_k^\delta )) …