Some topics on weighted Moore-Penrose inverse, weighted least squares and weighted regularized Tikhonov problems

DOI10.1016/j.amc.2003.08.035zbMath1064.65032OpenAlexW1995375949MaRDI QIDQ1888517

Dingkun Wang

Publication date: 23 November 2004

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

Full work available at URL: https://doi.org/10.1016/j.amc.2003.08.035

zbMATH Keywords

Condition numberGeneralized weighted singular value decompositionNearness to rank deficiencyStructured condition numberWeighted linear least squares problemWeighted Moore--Penrose inverse

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Theory of matrix inversion and generalized inverses (15A09) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)

Related Items (9)

Vector least-squares solutions for coupled singular matrix equations ⋮ Weighted \(UDV^*\)-decomposition and weighted spectral decomposition for rectangular matrices and their applications ⋮ Numerical range for weighted Moore-Penrose inverse of tensor ⋮ On convergents infinite products and some generalized inverses of matrix sequences ⋮ Representations and expansions of weighted pseudoinverse matrices, iterative methods, and problem regularization. I. positive definite weights ⋮ The representation and approximation for the weighted Minkowski inverse in Minkowski space ⋮ Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix ⋮ Weighted least squares solutions to general coupled Sylvester matrix equations ⋮ Reliability analysis of computer solutions of systems of linear algebraic equations with approximate initial data

Cites Work

• Condition numbers and their condition numbers
• Condition numbers and perturbation of the weighted Moore--Penrose inverse and weighted linear least squares problem.
• Weighted Tikhonov filter matrices for ill-posed problems.
• Expression for the perturbation of the weighted Moore-Penrose inverse
• Perturbation identities for regularized Tikhonov inverses and weighted pseudo- inverses
• The weighted Moore-Penrose inverse of modified matrices
• PCR algorithm for parallel computing minimum-norm \((T)\) least-squares \((S)\) solution of inconsistent linear equations
• The representation and approximation for the weighted Moore-Penrose inverse in Hilbert space.
• Generalized inverses. Theory and applications.
• Generalizing the Singular Value Decomposition
• Recurrent neural networks for computing weighted Moore-Penrose inverse
• Successive matrix squaring algorithm for parallel computing the weighted generalized inverse \(A^+_{MN}\)
• Representations for Moore-Penrose inverses in Hilbert spaces

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