On the perturbation of the least squares solutions in Hilbert spaces

DOI10.1016/0024-3795(94)90418-9zbMath0817.47017OpenAlexW2085775871WikidataQ127861658 ScholiaQ127861658MaRDI QIDQ1344079

V. Pereyra

Publication date: 9 February 1995

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

Full work available at URL: https://doi.org/10.1016/0024-3795(94)90418-9

zbMATH Keywords

perturbation analysisoperator equationleast squares solutions

Mathematics Subject Classification ID

Perturbation theory of linear operators (47A55) Equations and inequalities involving linear operators, with vector unknowns (47A50)

Related Items (26)

Perturbation of the Moore–Penrose Metric generalized inverse with applications to the best approximate solution problem in L^p(Ω, μ) ⋮ Perturbation analysis of generalized inverses of linear operators in Banach spaces ⋮ Invariances of frame sequences under perturbations ⋮ The Structure of the Set of Extremal Solutions of Ill-Posed Operator EquationTx = ywith codimR(T) = 1 ⋮ On the continuity of generalized inverses of linear operators in Hilbert spaces. ⋮ Perturbation analysis for the operator equation \(Tx=b\) in Banach spaces ⋮ Invertibility and stability of linear combinations ofm-potent operators ⋮ On the perturbation bounds of g-inverses and oblique projections ⋮ Perturbation analysis of the least squares solution in Hilbert spaces ⋮ Perturbation and expression for inner inverses in Banach spaces and its applications ⋮ On the perturbation of the reduced minimum modulus of bounded linear operators. ⋮ On perturbations for oblique projection generalized inverses of closed linear operators in Banach spaces ⋮ Perturbations and expressions for generalized inverses in Banach spaces and Moore-Penrose inverses in Hilbert spaces of closed linear operators ⋮ Perturbation analysis for the reduced minimum modulus of bounded linear operator in Banach spaces. ⋮ On stable perturbations for outer inverses of linear operators in Banach spaces ⋮ Unnamed Item ⋮ A generalization of a classic theorem in the perturbation theory for linear operators ⋮ On the Stable Perturbation and Nashed’s Condition for Generalized Inverses^† ⋮ Perturbation analysis for the (skew) Hermitian matrix least squares problem \(AXA^H=B\) ⋮ Representations for Moore-Penrose inverses in Hilbert spaces ⋮ Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces ⋮ Some properties of unbounded operators with closed range ⋮ Closed \(EP\) and hypo-\(EP\) operators on Hilbert spaces ⋮ Perturbation of least squares problem in Hilbert spaces. ⋮ Minimal distance upper bounds for the perturbation of least squares problems in Hilbert spaces ⋮ New perturbation results on pseudo-inverses of linear operators in Banach spaces

Cites Work

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• On the error estimate for the projection of a point onto a linear manifold
• Perturbation of the least squares problem
• The perturbation of consistent least squares problems
• Perturbation analysis for the projection of a point to an affine set
• Inner, outer, and generalized inverses in banach and hilbert spaces
• Approximations to Generalized Inverses of Linear Operators
• Perturbation theory for generalized and constrained linear least squares
• On the Continuity of the Generalized Inverse
• The Pseudo-Inverse of a Product
• Perturbation theory for pseudo-inverses

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