On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems

DOI10.1007/BF01739820zbMath0848.65026OpenAlexW2073148407MaRDI QIDQ1907867

Mårten Gulliksson

Publication date: 27 October 1996

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01739820

zbMATH Keywords

instabilitynumerical resultsfactorizationGram-Schmidt algorithmreorthogonalizationweighted linear least squares problems

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Orthogonalization in numerical linear algebra (65F25)

Related Items

Minimal polynomial and reduced rank extrapolation methods are related ⋮ Effective condition number for weighted linear least squares problems and applications to the Trefftz method ⋮ Condition numbers for a linear function of the solution to the constrained and weighted least squares problem and their statistical estimation ⋮ Stability of the MGS-like elimination method for equality constrained least squares problems ⋮ Numerical stability of orthogonalization methods with a non-standard inner product ⋮ Efficient implementations of the modified Gram-Schmidt orthogonalization with a non-standard inner product ⋮ Cholesky-Like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms ⋮ Some new properties of the equality constrained and weighted least squares problem

Cites Work

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• Numerics of Gram-Schmidt orthogonalization
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• Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm
• Modifying the QR-Decomposition to Constrained and Weighted Linear Least Squares
• Backward Error Analysis for the Constrained and Weighted Linear Least Squares Problem When Using the Weighted $QR$ Factorization
• Iterative refinement of linear least squares solutions I