Scale-type-estimates for a generalized method of Lavrent'ev regularization

J. Janno 1  and U. Tautenhahn 2
  • 1 Tallinn Technical University, Institute of Mathematics, Ehitajate tee 5, 19086 Tallinn, Estonia. E-mail: janno@ioc.ee
  • 2 University of Applied Sciences Zittau/Görlitz, Department of Mathematics, P.O. Box 1455, 02755 Zittau, Germany. E-mail: u.tautenhahn@hs-zigr.de

A generalized method of Lavrent'ev regularization involving an unbounded operator is studied. Assuming source condition in terms of the inverse of the unbounded operator, error estimates of scale type for the regularized solution are derived. The method is applied to ill-posed problems containing selfadjoint operators and Volterra equations of the first kind.

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This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems. These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse problem solutions are also published.

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