On the reduction of Tikhonov minimization problems and the construction of regularization matrices

DOI10.1007/s11075-012-9600-zzbMath1254.65049OpenAlexW2003211941MaRDI QIDQ715132

L. Dykes, Lothar Reichel

Publication date: 1 November 2012

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9600-z

zbMATH Keywords

numerical examplessingular value decompositionTikhonov regularizationill-posed problemregularization matrixpenalized least-squares problem

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22)

Related Items (7)

A Tikhonov regularized penalty function approach for solving polylinear programming problems ⋮ Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches ⋮ Tikhonov regularization via flexible Arnoldi reduction ⋮ Simplified GSVD computations for the solution of linear discrete ill-posed problems ⋮ Square smoothing regularization matrices with accurate boundary conditions ⋮ Rescaling the GSVD with application to ill-posed problems ⋮ Dynamic force identification problem based on a novel improved Tikhonov regularization method

Uses Software

• Regularization tools
• ErresTools

Cites Work

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• Invertible smoothing preconditioners for linear discrete ill-posed problems
• Simple square smoothing regularization operators
• Error estimates for linear systems with applications to regularization
• Error estimates for the regularization of least squares problems
• Extrapolation techniques for ill-conditioned linear systems
• Multi-parameter regularization techniques for ill-conditioned linear systems
• Regularization, GSVD and truncated GSVD
• A weighted pseudoinverse, generalized singular values, and constrained least squares problems
• Regularization tools version \(4.0\) for matlab \(7.3\)
• Orthogonal projection regularization operators
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• Algorithms for the regularization of ill-conditioned least squares problems
• Computing the Generalized Singular Value Decomposition

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