Author: Heinz W. Engl
Abstract: Inverse problems where one looks for causes for desired or observed effects, are usually ill-posed, i.e. their solution is not unique and/or unstable with respect to data perturbations. We give many examples from (also, but not exclusively, industrial) applications where inverse problems need to be solved. The paper concentrates on describing the mathematical framework for studying regularization methods, which are needed for the stable numerical solution of ill-posed problems.