Simplified GSVD computations for the solution of linear discrete ill-posed problems

DOI10.1016/j.cam.2013.04.019zbMath1291.65117OpenAlexW2165344682MaRDI QIDQ2252680

L. Dykes, Lothar Reichel

Publication date: 23 July 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2013.04.019

zbMATH Keywords

Tikhonov regularizationill-posed problemgeneralized singular value decompositionTGSVD

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (17)

On the computation of a truncated SVD of a large linear discrete ill-posed problem ⋮ Circulant preconditioners for discrete ill-posed Toeplitz systems ⋮ On the choice of solution subspace for nonstationary iterated Tikhonov regularization ⋮ Optimal Low-rank Approximations of Bayesian Linear Inverse Problems ⋮ Parameter determination for Tikhonov regularization problems in general form ⋮ Adaptive cross approximation for Tikhonov regularization in general form ⋮ Numerical considerations of block GMRES methods when applied to linear discrete ill-posed problems ⋮ Goal-Oriented Optimal Approximations of Bayesian Linear Inverse Problems ⋮ The structure of iterative methods for symmetric linear discrete ill-posed problems ⋮ The GSVD: Where are the Ellipses?, Matrix Trigonometry, and More ⋮ Some properties of range restricted GMRES methods ⋮ Bayes Meets Krylov: Statistically Inspired Preconditioners for CGLS ⋮ Generalized singular value decomposition with iterated Tikhonov regularization ⋮ 3D temperature distribution reconstruction in furnace based on acoustic tomography ⋮ Tikhonov Regularization and Randomized GSVD ⋮ Arnoldi decomposition, GMRES, and preconditioning for linear discrete ill-posed problems ⋮ Localization of impact on box mechanical structure by the method of modal parameters extraction combined with K-means clustering

Uses Software

• Regularization tools
• ErresTools

Cites Work

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• Orthogonal projection regularization operators
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• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• Computing the Generalized Singular Value Decomposition

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