Numerics of Gram-Schmidt orthogonalization
From MaRDI portal
Publication:1319993
DOI10.1016/0024-3795(94)90493-6zbMath0801.65039OpenAlexW2052087587MaRDI QIDQ1319993
Publication date: 19 April 1994
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)90493-6
Gram-Schmidt orthogonalizationstability of algorithmBlock Gram-Schmidt algorithmsHouseholder \(QR\) factorization
Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25)
Related Items (48)
GPMR: An Iterative Method for Unsymmetric Partitioned Linear Systems ⋮ Unnamed Item ⋮ Rank-\(k\) modification methods for recursive least squares problems ⋮ Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids ⋮ Perturbation analysis of the canonical correlations of matrix pairs ⋮ Orthogonal matrix and its application in Bloom's threshold scheme ⋮ An efficient QR based method for the computation of Lyapunov exponents ⋮ A four-wing hyper-chaotic attractor generated from a 4-D memristive system with a line equilibrium ⋮ Numerical stability of GMRES ⋮ On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems ⋮ Meshfree Methods: A Comprehensive Review of Applications ⋮ New interpretation of related Huang's methods ⋮ Ordered modified Gram-Schmidt orthogonalization revised ⋮ Some investigations on convergence of GMRES in solving BEM equations for slender beam structures ⋮ Krylov subspaces recycling based model order reduction for acoustic BEM systems and an error estimator ⋮ A fully implicit, compact finite difference method for the numerical solution of unsteady laminar flames ⋮ Intrinsically parallel solution of systems of linear partial differential equations ⋮ Iterative methods for the computation of a few eigenvalues of a large symmetric matrix ⋮ A randomized algorithm for the decomposition of matrices ⋮ Householder Orthogonalization with a Nonstandard Inner Product ⋮ Reorthogonalized block classical Gram-Schmidt ⋮ Ultra-high dimensional variable screening via Gram-Schmidt orthogonalization ⋮ Extrapolating the Arnoldi Algorithm To Improve Eigenvector Convergence ⋮ Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers ⋮ Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms ⋮ Optimal symplectic Householder transformations for \(SR\) decomposition ⋮ The influence of orthogonality on the Arnoldi method ⋮ A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting ⋮ Numerical stability of orthogonalization methods with a non-standard inner product ⋮ Analysis of the self projected matching pursuit algorithm ⋮ Randomized preprocessing of homogeneous linear systems of equations ⋮ Diffusion wavelets ⋮ An automatic Krylov subspaces recycling technique for the construction of a global solution basis of non-affine parametric linear systems ⋮ On direct elimination methods for solving the equality constrained least squares problem ⋮ On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms ⋮ Affine tensor product model transformation ⋮ Functional variable selection via Gram–Schmidt orthogonalization for multiple functional linear regression ⋮ A two-directional Arnoldi process and its application to parametric model order reduction ⋮ Class-Incremental Generalized Discriminant Analysis ⋮ Parameter Identification and Model-Based Control of Redundantly Actuated, Non-holonomic, Omnidirectional Vehicles ⋮ More robust Chebyshev filtering for SCF iteration, with applications in real-space DFT ⋮ Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling ⋮ A Randomized Blocked Algorithm for Efficiently Computing Rank-revealing Factorizations of Matrices ⋮ Robust and Accurate Stopping Criteria for Adaptive Randomized Sampling in Matrix-Free Hierarchically Semiseparable Construction ⋮ Block Modified Gram--Schmidt Algorithms and Their Analysis ⋮ ANALYSIS OF DIFFERENT PARTITIONING SCHEMES FOR PARALLEL GRAM-SCHMIDT ALGORITHMS ⋮ Improved Gram-Schmidt type downdating methods ⋮ One-sided reduction to bidiagonal form
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- 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
- Elimination with weighted row combinations for solving linear equations and least squares problems
- Jordan-Elimination und Ausgleichung nach kleinsten Quadraten
- Stability Analysis and Improvement of the Block Gram–Schmidt Algorithm
- A Storage-Efficient $WY$ Representation for Products of Householder Transformations
- Solutions to Weighted Least Squares Problems by Modified Gram-Schmidt with Iterative Refinement
- Modified gram-schmidt process vs. classical gram-schmidt
- 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
- Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
- The least squares problem and pseudo-inverses
- A Report on the Accuracy of Some Widely Used Least Squares Computer Programs
- Experiments on Gram-Schmidt Orthogonalization
- Round off error analysis for Gram-Schmidt method and solution of linear least squares problems
This page was built for publication: Numerics of Gram-Schmidt orthogonalization