ABSTRACT
A peculiar feature of ill-posed problems is the great variety of methods which have been proposed and are used for their solution. The definition of a regularization algorithm introduced by A.N. Tikhonov [1,2] provides a rather general setting for describing most of these methods, at least the deterministic ones, i.e. the methods where statistical properties of the data and of the solution are not used. This definition, however, even if it shows important relationships between methods for solving ill-posed problems and approximation theory, does not explain why so many different methods can be used for solving the same problem and why this situation is necessary and desirable.
