The loss of orthogonality in the Gram-Schmidt orthogonalization process
From MaRDI portal
Publication:815235
DOI10.1016/j.camwa.2005.08.009zbMath1085.65037OpenAlexW2087891564MaRDI QIDQ815235
Julien Langou, Miroslav Rozložnik, Luc Giraud
Publication date: 16 February 2006
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2005.08.009
parallel computationGram-Schmidt orthogonalizationQR factorizationrounding error analysisreorthogonalization
Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25)
Related Items
Experiments on orthogonalization by biorthogonal representations of orthogonal projectors, Analysis of the effects of a pulsed electromagnetic field on the dynamic response of electrically conductive composites, The RSRR method for solving large-scale nonlinear eigenvalue problems in boundary element method, Model-order reduction of coupled DAE systems via \(\varepsilon\) technique and Krylov subspace method, Schur complement-based domain decomposition preconditioners with low-rank corrections, A novel parallel algorithm based on the Gram-Schmidt method for tridiagonal linear systems of equations, Statistical properties of BayesCG under the Krylov prior, Deflation for the Off-Diagonal Block in Symmetric Saddle Point Systems, A family of three-dimensional virtual elements for Hellinger-Reissner elasticity problems, On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations, Certified reduced basis approximation for the coupling of viscous and inviscid parametrized flow models, GMRES algorithms over 35 years, Uncertainty quantification for nonlinear difference equations with dependent random inputs via a stochastic Galerkin projection technique, Numerical convergence of the Lyapunov spectrum computed using low Mach number solvers, An improved algorithm for the multidimensional moment-constrained maximum entropy problem, On the convergence of Krylov methods with low-rank truncations, Improved adaptive control for the discrete‐time parametric‐strict‐feedback form, Coupled BE-FE based vibroacoustic modal analysis and frequency sweep using a generalized resolvent sampling method, Unsupervised streaming anomaly detection for instrumented infrastructure, Numerical stability of orthogonalization methods with a non-standard inner product, Analysis of the self projected matching pursuit algorithm, Communication lower bounds and optimal algorithms for numerical linear algebra, The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling, An efficient solution of system of generalized Abel integral equations using Bernstein polynomials wavelet bases, Error analysis of an incremental proper orthogonal decomposition algorithm for PDE simulation data, Arnoldi method for large quaternion right eigenvalue problem, A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems, Convergence acceleration of iterative algorithms. Applications to thin shell analysis and Navier-Stokes equations, On the convergence of adaptive gPC for non-linear random difference equations: Theoretical analysis and some practical recommendations, The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software, A new projected variant of the deflated block conjugate gradient method, Combining polynomial chaos expansions and the random variable transformation technique to approximate the density function of stochastic problems, including some epidemiological models, Randomized Gram--Schmidt Process with Application to GMRES
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Iterative algorithms for Gram-Schmidt orthogonalization
- A new look at the Lanczos algorithm for solving symmetric systems of linear equations
- Parallel implementation of a multiblock method with approximate subdomain solution
- Numerical behaviour of the modified Gram-Schmidt GMRES implementation
- Rounding error analysis of the classical Gram-Schmidt orthogonalization process
- Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm
- Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
- Solving linear least squares problems by Gram-Schmidt orthogonalization
- Round off error analysis for Gram-Schmidt method and solution of linear least squares problems