Details

Autor(en) / Beteiligte

• Leonov, A. S.

Titel

Regularizing algorithms with optimal and extra-optimal quality

Ist Teil von

• Numerical analysis and applications, 2016-10, Vol.9 (4), p.288-298

Ort / Verlag

Moscow: Pleiades Publishing

Erscheinungsjahr

2016

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• The notion of a special quality for approximate solutions to ill-posed inverse problems is introduced. A posteriori estimates of the quality are studied for different regularizing algorithms. Examples of typical quality functionals are provided, which arise in solving linear and nonlinear inverse problems. A technique and a numerical algorithm for calculating a posteriori quality estimates for approximate solutions of general nonlinear inverse problems are developed. New notions of optimal and extra-optimal quality of a regularizing algorithm are introduced. The theory of regularizing algorithms with optimal and extra-optimal quality is presented, which includes an investigation of optimal properties for estimation functions of the quality. Examples of regularizing algorithms with extra-optimal quality of solutions are given, as well as examples of regularizing algorithms without such a property. Results of numerical experiments illustrate a posteriori quality estimation.