Error analysis of QR decompositions by Givens transformations

DOI10.1016/0024-3795(75)90068-3zbMath0308.65022OpenAlexW2134688242MaRDI QIDQ1218717

W. M. Gentleman

Publication date: 1975

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

Full work available at URL: https://doi.org/10.1016/0024-3795(75)90068-3

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (20)

Linear algebra on high performance computers ⋮ Hybrid algorithm for fast Toeplitz orthogonalization ⋮ Error analysis of algorithms for computing the projection of a point onto a linear manifold ⋮ A survey of the advances in the exploitation of the sparsity in the solution of large problems ⋮ Asymptotic normality of multivariate trimmed means ⋮ Multivariate \(\theta\)-generalized normal distributions ⋮ On the error estimate for the projection of a point onto a linear manifold ⋮ Comparison of two pivotal strategies in sparse plane rotations ⋮ Rounding-error and perturbation bounds for the indefinite QR factorization ⋮ An optimal, stable continued fraction algorithm for arbitrary dimension ⋮ Performing armchair roundoff analyses of statistical algorithms ⋮ A fast algorithm for index of annihilation computations ⋮ Stability analysis of the method of seminormal equations for linear least squares problems ⋮ Implicit standard Jacobi gives high relative accuracy ⋮ An alternative Givens ordering ⋮ Error analysis of an algorithm for solving an undetermined linear system ⋮ Error analysis of null space algorithm for linear equality constrained least squares problems ⋮ Stability analysis of the G-algorithm and a note on its applications to sparse least squares problems ⋮ A pipelined Givens method for computing the QR factorization of a sparse matrix ⋮ A direct method for completing eigenproblem solutions on a parallel computer

Cites Work

• Least Squares Computations by Givens Transformations Without Square Roots
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