Perturbation bound of singular linear systems

DOI10.1016/S0096-3003(99)00120-4zbMath1022.65042MaRDI QIDQ1569082

Yi-Min Wei

Publication date: 25 June 2000

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

zbMATH Keywords

weighted Moore-Penrose inversecomponentwise perturbationweighted linear least squares problemsingular linear algebraic system

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09)

Related Items (12)

Vector least-squares solutions for coupled singular matrix equations ⋮ Condition numbers and perturbation of the weighted Moore--Penrose inverse and weighted linear least squares problem. ⋮ On convergents infinite products and some generalized inverses of matrix sequences ⋮ The representation and approximation for the weighted Minkowski inverse in Minkowski space ⋮ Successive matrix squaring algorithm for parallel computing the weighted generalized inverse \(A^+_{MN}\) ⋮ Extension and generalization properties of the weighted Minkowski inverse in a Minkowski space for an arbitrary matrix ⋮ The condition numbers for weighted Moore-Penrose inverse and weighted linear least squares problem ⋮ Expression for the perturbation of the weighted Moore-Penrose inverse ⋮ The representation and approximation for the weighted Moore-Penrose inverse ⋮ 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.

Cites Work

• Component-wise perturbation analysis and error bounds for linear least squares solutions
• The perturbation of consistent least squares problems
• On the augmented system approach to sparse least-squares problems
• New perturbation results for equality-constrained least squares problems
• Scaling for Numerical Stability in Gaussian Elimination
• Improved Error Bounds for Underdetermined System Solvers
• Generalizing the Singular Value Decomposition
• Inverse Order Rule for Weighted Generalized Inverse
• On the Continuity of the Generalized Inverse
• Recurrent neural networks for computing weighted Moore-Penrose inverse
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