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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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On reduction of informational expenses in solving ill-posed problems with not exactly given input data

S. G. Solodky1 / E. V. Lebedeva2

1Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshscenkivska Str. 3, 01601 Kiev, Ukraine. Email: solodky@imath.kiev.ua

2Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshscenkivska Str. 3, 01601 Kiev, Ukraine. Email: djecsa@imath.kiev.ua

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 16, Issue 2, Pages 195–207, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/JIIP.2008.012, May 2008

Publication History

Received:
2006-08-10
:
2007-02-14
Published Online:
2008-05-09

Abstract

A class of approximate methods to solve operator equations of first kind with not exactly given input data is constructed. For involved methods their optimality by the order on sets of sourcewise represented solutions is proved and the bound of informational expenses is obtained. These algorithms are numerically implemented in an efficient way. An example of application of two such algorithms is given.

Key words.: Ill-posed problems; regularization method; discretization; projection scheme; discrepancy principle

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