Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices

DOI10.1016/S0024-3795(00)00018-5zbMath0957.15014MaRDI QIDQ1976905

Froilán M. Dopico, Julio Moro, Juan M. Molera

Publication date: 20 March 2001

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

zbMATH Keywords

singular valuessingular vectorsperturbation boundeigenvalue perturbationeigenvector perturbationHermitean matrices

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (6)

On the variation of the spectrum of a Hermitian matrix ⋮ Optimal perturbation bounds for the Hermitian eigenvalue problem ⋮ A note on the perturbation bounds of eigenspaces for Hermitian matrices ⋮ Relative perturbation bounds for eigenpairs of diagonalizable matrices ⋮ Numerical methods for accurate computation of the eigenvalues of Hermitian matrices and the singular values of general matrices ⋮ Relative perturbation theory for a class of diagonalizable Hermitian matrix pairs

Cites Work

• The Lidskii-Mirsky-Wielandt theorem -- additive and multiplicative versions
• Floating-point perturbations of Hermitian matrices
• An overview of relative \(\sin\Theta\) theorems for invariant subspaces of complex matrices
• Perturbation theory for linear operators.
• Matrix Analysis
• Jacobi’s Method is More Accurate than QR
• Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
• Three Absolute Perturbation Bounds for Matrix Eigenvalues Imply Relative Bounds
• Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
• Spectral Perturbation Bounds for Positive Definite Matrices
• On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure
• Accurate Eigensystem Computations by Jacobi Methods
• Relative Perturbation Techniques for Singular Value Problems
• Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
• Perturbation bounds in connection with singular value decomposition
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