Modified Gram-Schmidt-based methods for block downdating the Cholesky factorization

DOI10.1016/j.cam.2010.09.003zbMath1213.65050OpenAlexW1987236893MaRDI QIDQ629427

Qiaohua Liu

Publication date: 9 March 2011

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

Full work available at URL: https://doi.org/10.1016/j.cam.2010.09.003

zbMATH Keywords

numerical experimentsrandom matricesCholesky factorizationnumerical stabilitysymmetric positive definite matrixblock downdatinghyperbolic modified Gram-Schmidt method

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Random matrices (algebraic aspects) (15B52) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (2)

A recursive three-stage least squares method for large-scale systems of simultaneous equations ⋮ Incomplete hyperbolic Gram-Schmidt-based preconditioners for the solution of large indefinite least squares problems

Uses Software

• LINPACK

Cites Work

• Unnamed Item
• Accurate downdating of a modified Gram-Schmidt QR decomposition
• Improved Gram-Schmidt type downdating methods
• Stabilized hyperbolic Householder transformations
• Hyperbolic Householder Transforms
• Stability Analysis of a Householder-Based Algorithm for Downdating the Cholesky Factorization
• Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm
• Accurate Downdating of Least Squares Solutions
• Block Downdating of Least Squares Solutions
• A Note on Downdating the Cholesky Factorization

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