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An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in hilbert scales
Published in
2003
Volume: 2003
   
Issue: 39
Pages: 2487 - 2499
Abstract
Recently, Tautenhahn and Hämarik (1999) have considered a monotone rule as a parameter choice strategy for choosing the regularization parameter while considering approximate solution of an ill-posed operator equation Tx=y, where T is a bounded linear operator between Hilbert spaces. Motivated by this, we propose a new discrepancy principle for the simplified regularization, in the setting of Hilbert scales, when T is a positive and selfadjoint operator. When the data y is known only approximately, our method provides optimal order under certain natural assumptions on the ill-posedness of the equation and smoothness of the solution. The result, in fact, improves an earlier work of the authors (1997). © 2003 Hindawi Publishing Corporation. All rights reserved.
About the journal
JournalInternational Journal of Mathematics and Mathematical Sciences
ISSN01611712
Open AccessYes