Algorithmic Approaches in Sets of Good Answers in Inverse Problems

摘要

A very short review of methods recently used for solving applied or theoretical inverse problems and which neither belong to the class of local methods (the most well-known local method is the least squares method) or to the class of el'fand-Levitan type methods is presented. It is shown how very ill-posed inverse problems can be replaced by a set of well-posed questions. Then it is shown how the structure of certain direct problems can suggest using Backlund transformations to construct an algorithm for solving the inverse problem.