Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems

DOI10.1016/0024-3795(92)90003-SzbMath0743.15008MaRDI QIDQ1183146

Musheng Wei

Publication date: 28 June 1992

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

constrained least squares problemweighted least squares problemalgebraic propertiessolution formulas

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Theory of matrix inversion and generalized inverses (15A09) Linear equations (linear algebraic aspects) (15A06)

Related Items (16)

Structures and uniqueness conditions of \(MK\)-weighted pseudoinverses ⋮ New perturbation results for equality-constrained least squares problems ⋮ Updating QR factorization procedure for solution of linear least squares problem with equality constraints ⋮ Partial condition number for the equality constrained linear least squares problem ⋮ Equality constrained least squares problem over quaternion field ⋮ A new technique of quaternion equality constrained least squares problem ⋮ Equivalent formulae for the supremum and stability of weighted pseudoinverses ⋮ Stability of the MGS-like elimination method for equality constrained least squares problems ⋮ On direct elimination methods for solving the equality constrained least squares problem ⋮ Perturbation bounds for least squares problems with equality constraints ⋮ Algebraic properties and perturbation results for the indefinite least squares problem with equality constraints ⋮ Condition numbers for the K-weighted pseudoinverse and their statistical estimation ⋮ Conditioning theory of the equality constrained quadratic programming and its applications ⋮ On the perturbation of least squares problems with equality constraints ⋮ Some new properties of the equality constrained and weighted least squares problem ⋮ Perturbation bounds for constrained and weighted least squares problems

Cites Work

• On the error estimate for the projection of a point onto a linear manifold
• A new theoretical approach for Prony's method
• Perturbation Analysis for the Generalized Singular Value Problem
• On the Method of Weighting for Equality-Constrained Least-Squares Problems
• The Direct Solution of Weighted and Equality Constrained Least-Squares Problems
• Error Analysis and Implementation Aspects of Deferred Correction for Equality Constrained Least Squares Problems
• Perturbation Theory for the Least Squares Problem with Linear Equality Constraints
• Towards a Generalized Singular Value Decomposition
• Generalizing the Singular Value Decomposition
• On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems
• Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
• The Rotation of Eigenvectors by a Perturbation. III
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