When modified Gram-Schmidt generates a well-conditioned set of vectors

DOI10.1093/imanum/22.4.521zbMath1027.65050OpenAlexW1966343138MaRDI QIDQ4787672

Luc Giraud, Julien Langou

Publication date: 12 May 2003

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/188d081a07c1afefc6e04d0cb0204d1dd5ab19bc

zbMATH Keywords

numerical experimentsorthogonalizationGram-Schmidt algorithmfloating point aritmethic

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Orthogonalization in numerical linear algebra (65F25)

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Gram-Schmidt orthogonalization: 100 years and more ⋮ Computing the Weighted Geometric Mean of Two Large-Scale Matrices and Its Inverse Times a Vector ⋮ Parallelization of the Rational Arnoldi Algorithm ⋮ An improved algorithm for the multidimensional moment-constrained maximum entropy problem ⋮ Fast Randomized Non-Hermitian Eigensolvers Based on Rational Filtering and Matrix Partitioning ⋮ Adaptive reduced basis strategy based on goal oriented error assessment for stochastic problems ⋮ Rounding error analysis of the classical Gram-Schmidt orthogonalization process ⋮ Stability Analysis of the Two-level Orthogonal Arnoldi Procedure ⋮ The multidimensional moment-constrained maximum entropy problem: A BFGS algorithm with constraint scaling ⋮ Error analysis of an incremental proper orthogonal decomposition algorithm for PDE simulation data ⋮ Block Gram-Schmidt algorithms and their stability properties

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