A method of estimating the accuracy of the solution of an inverse problem without using a uniqueness theorem (Q1323941)

The following inverse problem is considered: determine the unknown coefficient in a mathematical model given by a boundary value problem assigned to a partial differential equation, provided the solution is known for all data (in a suitable class). An iterative method (which of course uses quite heavily solving the direct problem) is presented which is suitable for higher dimensions but requires a uniqueness result only for dimension one. Error estimates are deduced in a general context for operator equations.