About a deficit in low-order convergence rates on the example of autoconvolution

DOI10.1080/00036811.2014.886107zbMath1312.65087OpenAlexW2011563751MaRDI QIDQ4982026

Bernd Hofmann, Steven K. Burger

Publication date: 23 March 2015

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-130630

zbMATH Keywords

inverse problemsconvergence rateTikhonov regularizationlocal well-posednessill-posednesssource conditionautoconvolution

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (14)

Nesterov’s accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional ⋮ A Discretizing Levenberg-Marquardt Scheme for Solving Nonlinear Ill-Posed Integral Equations ⋮ On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case ⋮ A numerical comparison of some heuristic stopping rules for nonlinear Landweber iteration ⋮ Deautoconvolution in the two-dimensional case ⋮ A Coefficient Inverse Problem with a Single Measurement of Phaseless Scattering Data ⋮ Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule ⋮ Case Studies and a Pitfall for Nonlinear Variational Regularization Under Conditional Stability ⋮ On ill-posedness concepts, stable solvability and saturation ⋮ Convergence results and low-order rates for nonlinear Tikhonov regularization with oversmoothing penalty term ⋮ Non-convex regularization of bilinear and quadratic inverse problems by tensorial lifting ⋮ Convergence analysis of (statistical) inverse problems under conditional stability estimates ⋮ A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data ⋮ Inexact Newton regularization combined with two-point gradient methods for nonlinear ill-posed problems ^*

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