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Licensed Unlicensed Requires Authentication Published by De Gruyter September 7, 2013

On iterative methods for solving ill-posed problems modeled by partial differential equations

  • J. Baumeister EMAIL logo and A. Leitão EMAIL logo

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.

Published Online: 2013-09-07
Published in Print: 2001-02

© 2013 by Walter de Gruyter GmbH & Co.

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