New model function methods for determining regularization parameters in linear inverse problems

DOI10.1016/j.apnum.2009.05.006zbMath1167.65367OpenAlexW2080591774MaRDI QIDQ2271399

Jijun Liu, Zewen Wang

Publication date: 7 August 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2009.05.006

zbMATH Keywords

convergenceregularization parametermodel functionIll-posed problemsmorozov discrepancy principle

Mathematics Subject Classification ID

Numerical solutions to equations with linear operators (65J10) 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 integral equations (65R32) Linear operators and ill-posed problems, regularization (47A52) Inverse problems for integral equations (45Q05)

Related Items

Exponential Tikhonov Regularization Method for Solving an Inverse Source Problem of Time Fractional Diffusion Equation, Simultaneous determination of the space-dependent source and the initial distribution in a heat equation by regularizing Fourier coefficients of the given measurements, On the Laplacian operation with applications in magnetic resonance electrical impedance imaging, A regularized optimization method for identifying the space-dependent source and the initial value simultaneously in a parabolic equation, Data regularization for a backward time-fractional diffusion problem, A directly numerical algorithm for a backward time-fractional diffusion equation based on the finite element method, Determination of a spacewise-dependent heat source by a logarithmic-type regularization method, A non-iterative method for recovering the space-dependent source and the initial value simultaneously in a parabolic equation, Multi-parameter Tikhonov regularization and model function approach to the damped Morozov principle for choosing regularization parameters, Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation, On convergents infinite products and some generalized inverses of matrix sequences, On the interface identification of free boundary problem by method of fundamental solution

Uses Software

• Regularization tools

Cites Work

• On a class of damped Morozov principles
• The discrete Picard condition for discrete ill-posed problems
• A model function method for determining the regularizing parameter in potential approach for the recovery of scattered wave
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Using the \(L\)-curve for determining optimal regularization parameters
• A parameter choice method for Tikhonov regularization
• Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
• Iterative choices of regularization parameters in linear inverse problems
• One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
• An improved model function method for choosing regularization parameters in linear inverse problems
• Non-convergence of the L-curve regularization parameter selection method
• Inverse Problems and Torricelli's Law
• Linear integral equations
• An introduction to the mathematical theory of inverse problems