  We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3],
[4]) for solving ill-posed reconstruction problems modeled by PDE's. We
consider linear time dependent problems of elliptic, hyperbolic and parabolic
types. Each iteration of the analyzed methods consists on the solution of a
well posed boundary (or initial) value problem. The iterations are described as
powers of affine operators, as in [4]. We give alternative convergence proofs
for the algorithms, using spectral theory and some functional analytical
results (see [5], [6]).
