  We investigate the iterative methods proposed by Maz'ya and Kozlov (see
[KM1], [KM2]) for solving ill-posed inverse problems modeled by partial
differential equations. We consider linear evolutionary problems of elliptic,
hyperbolic and parabolic types. Each iteration of the analyzed methods consists
in the solution of a well posed problem (boundary value problem or initial
value problem respectively). The iterations are described as powers of affine
operators, as in [KM2]. We give alternative convergence proofs for the
algorithms by using spectral theory and the fact that the linear parts of these
affine operators are non-expansive with additional functional analytical
properties (see [Le1,2]). Also problems with noisy data are considered and
estimates for the convergence rate are obtained under a priori regularity
assumptions on the problem data.
