Weighted Tikhonov filter matrices for ill-posed problems.

DOI10.1016/S0096-3003(03)00149-8zbMath1042.65032OpenAlexW1983899315MaRDI QIDQ1427877

Michael Kwok-Po Ng, Yi-Min Wei

Publication date: 14 March 2004

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(03)00149-8

zbMATH Keywords

numerical exampleill-posed problemssignal reconstructionweighted pseudoinverseweighted Tikhonov regularizationrank deficientfilter matricesTikhonov matricesweighted filters

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (4)

Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems ⋮ Interval iterative methods for computing Moore-Penrose inverse ⋮ Computing Moore-Penrose inverses of Toeplitz matrices by Newton's iteration ⋮ Displacement structure of weighted pseudoinverses

Cites Work

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• Equivalence of regularization and truncated iteration in the solution of ill-posed image reconstruction problems
• Expression for the perturbation of the weighted Moore-Penrose inverse
• Perturbation identities for regularized Tikhonov inverses and weighted pseudo- inverses
• Perturbation bounds for constrained and weighted least squares problems
• The representation and approximation for the weighted Moore-Penrose inverse
• The Use and Properties of Tikhonov Filter Matrices
• Generalizing the Singular Value Decomposition
• The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
• Perturbation theory for pseudo-inverses

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