A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting
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Publication:1978115
DOI10.1016/S0024-3795(00)00022-7zbMath0990.65047MaRDI QIDQ1978115
Publication date: 18 July 2002
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
algorithmerror analysisleast-squares algorithmcolumn pivotingQR-factorizationreorthogonalizationmodified Gram-Schmidt method
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25)
Related Items (7)
Gram-Schmidt orthogonalization: 100 years and more ⋮ An improved algorithm for the multidimensional moment-constrained maximum entropy problem ⋮ Effectively Subsampled Quadratures for Least Squares Polynomial Approximations ⋮ Rounding error analysis of the classical Gram-Schmidt orthogonalization process ⋮ Loss and retention of accuracy in affine scaling methods ⋮ The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling ⋮ The orthogonal Rayleigh quotient iteration (ORQI) method
Uses Software
Cites Work
- Numerical aspects of Gram-Schmidt orthogonalization of vectors
- Iterative algorithms for Gram-Schmidt orthogonalization
- A new look at the Lanczos algorithm for solving symmetric systems of linear equations
- Numerics of Gram-Schmidt orthogonalization
- Numerical methods for solving linear least squares problems
- Loss and retention of accuracy in affine scaling methods
- Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm
- Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
- Experiments on Error Growth Associated with Some Linear Least-Squares Procedures
- Solving linear least squares problems by Gram-Schmidt orthogonalization
- Experiments on Gram-Schmidt Orthogonalization
- Round off error analysis for Gram-Schmidt method and solution of linear least squares problems
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