Heuristic parameter selection based on functional minimization: Optimality and model function approach

DOI10.1090/S0025-5718-2013-02674-9zbMath1278.65083MaRDI QIDQ2840624

Shuai Lu, Peter Mathé

Publication date: 23 July 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

inverse problemHilbert spacenumerical experimentserror boundTikhonov regularizationill-posed problemlinear operator equationlinear compact operatorheuristic parameter choiceHanke-Raus type rulemodified L-curve method

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Linear operators and ill-posed problems, regularization (47A52) Numerical solution to inverse problems in abstract spaces (65J22)

Related Items (5)

Heuristic Parameter Choice in Tikhonov Method from Minimizers of the Quasi-Optimality Function ⋮ A Bayesian interpretation of the L-curve ⋮ Regularized collocation in distribution of diffusion times applied to electrochemical impedance spectroscopy ⋮ A simplified L-curve method as error estimator ⋮ Parameter Choices for Fast Harmonic Spline Approximation

Uses Software

• Regularization tools

Cites Work

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• On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data
• Fixed-point iterations in determining the Tikhonov regularization parameter
• The quasi-optimality criterion for classical inverse problems
• Modulus of continuity for conditionally stable ill-posed problems in Hilbert space
• Dual Regularized Total Least Squares And Multi-Parameter Regularization
• Model functions in the modified L -curve method—case study: the heat flux reconstruction in pool boiling
• An improved fixed-point algorithm for determining a Tikhonov regularization parameter
• On the Choice of the Regularization Parameter in Nonlinear Inverse Problems
• Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
• Iterative choices of regularization parameters in linear inverse problems
• An improved model function method for choosing regularization parameters in linear inverse problems
• Saturation of Regularization Methods for Linear Ill-Posed Problems in Hilbert Spaces
• A Regularization Parameter in Discrete Ill-Posed Problems
• A General Heuristic for Choosing the Regularization Parameter in Ill-Posed Problems

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