An approach of orthogonalization within the Gram-Schmidt algorithm

DOI10.1007/s40314-016-0389-6zbMath1398.65073OpenAlexW2541049917MaRDI QIDQ725754

D. Kharzeev

Publication date: 2 August 2018

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-016-0389-6

zbMATH Keywords

ill-conditioned matrixGram-Schmidt algorithmloss of orthogonalityoptimized Gram-Schmidt algorithmreorthogonalization

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Inverse problems in linear algebra (15A29) Canonical forms, reductions, classification (15A21) Orthogonalization in numerical linear algebra (65F25)

Uses Software

• mctoolbox

Cites Work

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• Rounding error analysis of the classical Gram-Schmidt orthogonalization process
• Jordan-Elimination und Ausgleichung nach kleinsten Quadraten
• Gram-Schmidt orthogonalization: 100 years and more
• Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
• Solving linear least squares problems by Gram-Schmidt orthogonalization
• Experiments on Gram-Schmidt Orthogonalization
• Numerical Linear Algebra
• Modern Error Analysis

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