Componentwise analysis of direct factorization of real symmetric and Hermitian matrices

DOI10.1016/S0024-3795(97)00334-0zbMath0894.65009MaRDI QIDQ1379115

Ivan Slapničar

Publication date: 16 August 1998

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

zbMATH Keywords

numerical exampleHermitian matriceserror boundsfactorization algorithmCholesky methodcomponentwise error analysis

Mathematics Subject Classification ID

Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (18)

A Kogbetliantz-type algorithm for the hyperbolic SVD ⋮ Factoring symmetric totally nonpositive matrices and inverses with a diagonal pivoting method ⋮ Three-level parallel J-Jacobi algorithms for Hermitian matrices ⋮ Componentwise error analysis for the block LU factorization of totally nonnegative matrices ⋮ 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 ⋮ Perturbation theory for the eigenvalues of factorised symmetric matrices ⋮ Rounding-error and perturbation bounds for the indefinite QR factorization ⋮ Quadratic convergence estimate of scaled iterates by \(J\)-symmetric Jacobi method ⋮ Relative residual bounds for indefinite Hermitian matrices ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ Implicit standard Jacobi gives high relative accuracy ⋮ A bound for the condition of a hyperbolic eigenvector matrix ⋮ Cholesky-Like Factorization of Symmetric Indefinite Matrices and Orthogonalization with Respect to Bilinear Forms ⋮ Highly accurate symmetric eigenvalue decomposition and hyperbolic SVD

Uses Software

• LAPACK

Cites Work

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