Indefinite QR factorization

DOI10.1007/s10543-006-0044-5zbMath1093.65029OpenAlexW2038664656MaRDI QIDQ2492728

Sanja Singer

Publication date: 14 June 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-006-0044-5

zbMATH Keywords

indefinite QR factorizationblock J-rotationsHermitian indefinite matriceszero diagonal elements

Mathematics Subject Classification ID

Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25)

Related Items (13)

A Kogbetliantz-type algorithm for the hyperbolic SVD ⋮ Stable and Efficient Computation of Generalized Polar Decompositions ⋮ Two-sided generalized hyperbolic QR factorization and its perturbation analysis ⋮ Three-level parallel J-Jacobi algorithms for Hermitian matrices ⋮ The hyperbolic Schur decomposition ⋮ Full block \(J\)-Jacobi method for Hermitian matrices ⋮ The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD ⋮ A GPU-based hyperbolic SVD algorithm ⋮ Novel modifications of parallel Jacobi algorithms ⋮ Orthosymmetric block reflectors ⋮ Perturbation analysis for the hyperbolic QR factorization ⋮ Block-oriented \(J\)-Jacobi methods for Hermitian matrices ⋮ Cholesky-Like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms

Cites Work

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• Matrices and indefinite scalar products
• On a new class of elementary matrices
• An analysis of the HR algorithm for computing the eigenvalues of a matrix
• Decomposition of a symmetric matrix
• A note on the existence of the hyperbolic singular value decomposition
• Rounding-error and perturbation bounds for the indefinite QR factorization
• Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
• J-Orthogonal Matrices: Properties and Generation
• A Schur Method for Low-Rank Matrix Approximation
• Analysis of the Diagonal Pivoting Method
• Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations
• Partial Pivoting Strategies for Symmetric Matrices

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