Title: Unsaturable methods for solving severely ill-posed problems

Authors: Sergei G. Solodky, Ganna Mosentsova

Addresses: Department of Approximation Theory, Institute of Mathematics (National Academy of Sciences), Tereschenkivska Str. 3, 01601 Kiev, Ukraine. ' Department of Approximation Theory, Institute of Mathematics (National Academy of Sciences), Tereschenkivska Str. 3, 01601 Kiev, Ukraine

Abstract: Considered here is the problem of an approximate solution of severely ill-posed problems represented in the form of linear operator equations of the first kind with approximately known right-hand sides and operators. For a class of the problems two methods of solving were constructed which consist in combination of Morozov|s discrepancy principle and a finite-dimensional version of the ordinary Tikhonov regularisation. It is shown that the methods provide for the optimal order of accuracy without saturation. The efficiency of the theoretical results is checked by test example.

Keywords: severely ill-posed problems; regularisation parameter; saturation effect; discrepancy principle; source condition; approximate solution; linear operator equations.

DOI: 10.1504/IJCSM.2009.027875

International Journal of Computing Science and Mathematics, 2009 Vol.2 No.3, pp.229 - 242

Published online: 13 Aug 2009 *

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