On the error estimate for the projection of a point onto a linear manifold

DOI10.1016/0024-3795(90)90241-4zbMath0704.65026OpenAlexW1996326067MaRDI QIDQ917221

Musheng Wei

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0024-3795(90)90241-4

zbMATH Keywords

projectionStabilitygeneralized inverseslinear manifoldrank deficiencyleast square problemround off error analysis

Mathematics Subject Classification ID

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

Related Items (11)

On the perturbation of the least squares solutions in Hilbert spaces ⋮ On the continuity of generalized inverses of linear operators in Hilbert spaces. ⋮ Finding the orthogonal projection of a point onto an affine subspace ⋮ New perturbation results for equality-constrained least squares problems ⋮ Perturbation bounds for the metric projection of a point onto a linear manifold in reflexive strictly convex Banach spaces ⋮ Perturbation analysis of the least squares solution in Hilbert spaces ⋮ Algebraic properties of the rank-deficient equality-constrained and weighted least squares problems ⋮ Perturbation analysis of the Moore-Penrose metric generalized inverse with applications ⋮ Perturbation bounds for least squares problems with equality constraints ⋮ On the perturbation of least squares problems with equality constraints ⋮ Perturbation analysis for the projection of a point to an affine set

Cites Work

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• Rang revealing QR factorizations
• Numeric computation of the projection of a point onto a polyhedron
• Error analysis of algorithms for computing the projection of a point onto a linear manifold
• A direct method for the general solution of a system of linear equations
• Error analysis of QR decompositions by Givens transformations
• An Interval Analysis Approach to Rank Determination in Linear Least Squares Problems
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
• Perturbation theory for pseudo-inverses

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