Unifying unitary and hyperbolic transformations

DOI10.1016/S0024-3795(00)00108-7zbMath0970.65042OpenAlexW1995386581WikidataQ126591688 ScholiaQ126591688MaRDI QIDQ1587284

Allan O. Steinhardt, Sanzheng Qiao, Adam W. Bojanczyk

Publication date: 7 October 2001

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(00)00108-7

zbMATH Keywords

reflectioncondition numbersgeneralized Cholesky factorizationHouseholder transformsignature matrixpivoting strategieseigenvalue algorithmsgeneralized rotationgeneralized unitary matrixhyperbolic transformation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hermitian, skew-Hermitian, and related matrices (15B57) Direct numerical methods for linear systems and matrix inversion (65F05) Conditioning of matrices (15A12) Orthogonalization in numerical linear algebra (65F25)

Related Items (5)

A recursive three-stage least squares method for large-scale systems of simultaneous equations ⋮ \(\mathbb G\)-reflectors: Analogues of Householder transformations in scalar product spaces ⋮ A new sequential data assimilation method ⋮ UTV Expansin pack: Special-purpose rank-revealing algorithms ⋮ An implicit Jacobi-like method for computing generalized hyperbolic SVD

Uses Software

• LINPACK

Cites Work

• Unnamed Item
• Matrices and indefinite scalar products
• Hyperbolic Householder Algorithms for Factoring Structured Matrices
• Hyperbolic householder transformations
• Hyperbolic Householder Transforms
• Stability Analysis of a Householder-Based Algorithm for Downdating the Cholesky Factorization
• The Effects of Rounding Error on an Algorithm for Downdating a Cholesky Factorization
• On Hyperbolic Triangularization: Stability and Pivoting
• A Note on Downdating the Cholesky Factorization

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