Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-monotone operators with application to autoconvolution equation

DOI10.1088/0266-5611/16/2/305zbMath1014.65038OpenAlexW1964786007MaRDI QIDQ4954082

Jaan Janno

Publication date: 17 July 2003

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/16/2/305

zbMATH Keywords

numerical examplesHilbert spaceerror estimatenonlinear operator equationill-posed problemsparameter choiceLavrent'ev regularizationautoconvolution equationnonlinear near-to-monotone operators

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for ill-posed problems for integral equations (65R30) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

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Lavrentiev's regularization method in Hilbert spaces revisited ⋮ Local regularization methods for inverse Volterra equations applicable to the structure of solid surfaces ⋮ Local regularization of nonlinear Volterra equations of Hammerstein type ⋮ On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case ⋮ Deautoconvolution in the two-dimensional case ⋮ Parallel regularized Newton method for nonlinear ill-posed equations ⋮ Error estimates for the regularization of optimal control problems with pointwise control and state constraints ⋮ Non-convex regularization of bilinear and quadratic inverse problems by tensorial lifting ⋮ Input identification to a class of nonlinear input-output causal systems ⋮ On Lavrentiev Regularization for Ill-Posed Problems in Hilbert Scales ⋮ On the Determination of a Density Function by Its Autoconvolution Coefficient ⋮ About a deficit in low-order convergence rates on the example of autoconvolution ⋮ A regularized variational inequality approach for nonlinear monotone ill-posed equations ⋮ Scale-type-estimates for a generalized method of Lavrent'ev regularization ⋮ Regularization of an autoconvolution problem in ultrashort laser pulse characterization

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