Greedy Tikhonov regularization for large linear ill-posed problems

DOI10.1080/00207160701356324zbMath1125.65034OpenAlexW2118403361MaRDI QIDQ5308815

Andriy Shyshkov, Hassane Sadok, Lothar Reichel

Publication date: 8 October 2007

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160701356324

zbMATH Keywords

numerical exampleinverse problemTikhonov regularizationdiscrepancy principleLanczos bidiagonalizationdiscrete ill-posed problemFredholm integral equation of the first kindleast-squares iterative method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Numerical methods for ill-posed problems for integral equations (65R30) Fredholm integral equations (45B05)

Related Items

Numerical results for linear Fredholm integral equations of the first kind over surfaces in three dimensions, A predictor-corrector iterated Tikhonov regularization for linear ill-posed inverse problems, An inexact non stationary Tikhonov procedure for large-scale nonlinear ill-posed problems, Square regularization matrices for large linear discrete ill-posed problems

Uses Software

• LSQR
• Regularization tools

Cites Work

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• Invertible smoothing preconditioners for linear discrete ill-posed problems
• A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations
• Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
• Regularization tools: A Matlab package for analysis and solution of discrete ill-posed problems
• Tikhonov regularization of large linear problems
• A note on Tikhonov regularization of large linear problems
• Tikhonov regularization and the L-curve for large discrete ill-posed problems
• Estimation of the \(L\)-curve via Lanczos bidiagonalization
• Iterative methods for ill-posed problems and semiconvergent sequences
• Improvement of the resolution of an instrument by numerical solution of an integral equation
• Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• A Bidiagonalization-Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• The Use of Auto-correlation for Pseudo-rank Determination in Noisy III-conditioned Linear Least-squares Problems
• Algorithms for the regularization of ill-conditioned least squares problems
• Fast CG-Based Methods for Tikhonov--Phillips Regularization
• Rank-Deficient and Discrete Ill-Posed Problems
• The regularizing properties of the adjoint gradient method in ill-posed problems