Structure in loss of orthogonality

DOI10.1016/j.laa.2020.07.024zbMath1467.65029OpenAlexW3044199524MaRDI QIDQ2029846

David Titley-Peloquin, Xiao-Wen Chang, Christopher C. Paige

Publication date: 4 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.laa.2020.07.024

zbMATH Keywords

eigenproblemsingular value decompositionJordan canonical formrounding error analysisLanczos processloss of orthogonality

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Roundoff error (65G50) Orthogonalization in numerical linear algebra (65F25)

Uses Software

• LSQR
• LSMR
• CRAIG

Cites Work

• Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
• Accuracy of Two Three-term and Three Two-term Recurrences for Krylov Space Solvers
• Sensitivity analysis of the Lanczos reduction
• Properties of a Unitary Matrix Obtained from a Sequence of Normalized Vectors
• An Augmented Stability Result for the Lanczos Hermitian Matrix Tridiagonalization Process
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• The Lanczos and conjugate gradient algorithms in finite precision arithmetic
• A Useful Form of Unitary Matrix Obtained from Any Sequence of Unit 2-Norm n-Vectors
• Matrix Analysis
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Loss and Recapture of Orthogonality in the Modified Gram–Schmidt Algorithm
• Accuracy of the Lanczos Process for the Eigenproblem and Solution of Equations
• Calculating the Singular Values and Pseudo-Inverse of a Matrix
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item