| Contents |
| The common approach of using the coefficient-to-state map within the operator equation formulation of an inverse problem has certain drawbacks from a computational point of view. In particular, each step in a solution by iteratively minimizing some Tikhonov functional or applying a regularized Gauss-Newton method will require more or less exact solution of the PDE. This can be avoided by all-at once formulations, where the PDE and the measurement equation are considered as one large system of equations which is solved simultaneously. This allows to safe a considerable amount of computational cost, especially in the context of nonlinear PDEs. In this talk we will particularly focus on all-at-once versions of regularized Newton type methods and their adaptive discretization using dual weighted residual estimators. |
|