Abstract - We investigate the iterative methods proposed by Maz’ya and Kozlov (see (6, 7)) 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 (7). 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 (9, 10)). Also problems with noisy data are considered and estimates for the convergence rate are obtained under a priori regularity assumptions on the problem data.
Journal of Inverse and III-posed Problems – de Gruyter
Published: Feb 1, 2001
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