Some efficient methods for solving non-linear inverse problems

The solution of non-linear inverse problems and the reliability testing of the solution may be impeded by noise in the data. Three methods are presented for addressing these problems. The first method recognizes that some parameters can be eliminated from the solution through sub-minimization. In the second method - to "clean" the merit-function - the concept of the closest noise-free merit-function (`follower') is introduced, which can be approximated by the real-life merit-function on a part of the parameter domain, on the condition that the shape of the noise-free merit-function is 'model invariant' being known a priori. In the third method the first method is used and it is shown that if all parameters are eliminated except one, then the transformed merit-function (depending on only one parameter) can be used for reliability testing. The complementary methods are illustrated by the example of the modification of the shark secant method and by the evaluation of a basic geotechnical test.