Ill-posedness and local ill-posedness concepts in hilbert spaces*

DOI10.1080/02331930008844503zbMath0981.65072OpenAlexW2076388469MaRDI QIDQ4512754

Bernd Hofmann

Publication date: 5 March 2002

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930008844503

zbMATH Keywords

Hilbert spacecompact operatorFréchet derivativeill-posed problemsill-posednessnonlinear inverse problemnonlinear and linear operator equations

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with linear operators (65J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52)

Related Items (4)

Parameter identification for elliptic boundary value problems: an abstract framework and applications ⋮ A fast subspace optimization method for nonlinear inverse problems in Banach spaces with an application in parameter identification ⋮ On ill-posedness concepts, stable solvability and saturation ⋮ Regularization of an autoconvolution problem in ultrashort laser pulse characterization

Cites Work

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• Well-posed optimization problems
• A convergence analysis of the Landweber iteration for nonlinear ill-posed problems
• Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
• Local ill-posedness and source conditions of operator equations in Hilbert spaces
• On autoconvolution and regularization
• Factors influencing the ill-posedness of nonlinear problems
• On the degree of ill-posedness for nonlinear problems

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