On Lavrentiev Regularization for Ill-Posed Problems in Hilbert Scales

DOI10.1081/NFA-120023870zbMath1063.65040OpenAlexW2025980351MaRDI QIDQ4435187

Jaan Janno, Ulrich Tautenhahn

Publication date: 26 November 2003

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/nfa-120023870

zbMATH Keywords

Hilbert spacelinear ill-posed problemsnonlinear ill-posed problemsmonotone operatorsinverse heat conduction problemregularization methodsHilbert scalesLavrentiev regularizationVolterra integral equation of the first kinda priori parameter choicesa posteriori parameter choices

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Heat equation (35K05) Inverse problems for PDEs (35R30) Nonlinear ill-posed problems (47J06) Numerical solutions to equations with linear operators (65J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for ill-posed problems for integral equations (65R30) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Linear operators and ill-posed problems, regularization (47A52)

Related Items (10)

Local convergence of the Lavrentiev method for the Cauchy problem via a Carleman inequality ⋮ A derivative-free iterative method for nonlinear ill-posed equations with monotone operators ⋮ Multiscale Lavrentiev method for systems of Volterra equations of the first kind ⋮ Impact of conditional stability: Convergence rates for general linear regularization methods ⋮ Two-step modified Newton method for nonlinear Lavrentiev regularization ⋮ Input identification to a class of nonlinear input-output causal systems ⋮ A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations ⋮ Unnamed Item ⋮ Newton Lavrentiev regularization for ill-posed operator equations in Hilbert scales ⋮ A scheme for stable numerical differentiation

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