Computable eigenvalue bounds for rank-\(k\) perturbations

DOI10.1016/j.laa.2010.02.010zbMath1195.15019OpenAlexW2037139389MaRDI QIDQ968983

Ricardo Reis da Silva, Jan H. Brandts

Publication date: 11 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.02.010

zbMATH Keywords

Hermitian matricessingular valueseigenvalue boundsarrowhead matrixbordered diagonallow rank Hermitian perturbations

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items

A Preconditioned MINRES Method for Optimal Control of Wave Equations and its Asymptotic Spectral Distribution Theory ⋮ A block Toeplitz preconditioner for all-at-once systems from linear wave equations ⋮ A sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEs ⋮ Preconditioning and Iterative Solution of All-at-Once Systems for Evolutionary Partial Differential Equations ⋮ Circulant preconditioners for functions of Hermitian Toeplitz matrices ⋮ An efficient method for computing the inverse of arrowhead matrices

Uses Software

• IPSEN

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing the eigenvalues and eigenvectors of symmetric arrowhead matrices
• Updating the partial singular value decomposition in latent semantic indexing
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• Rank-one modification of the symmetric eigenproblem
• Matrices with prescribed Ritz values
• QR-Like Algorithms for Symmetric Arrow Matrices
• Using Linear Algebra for Intelligent Information Retrieval
• Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices
• Some Modified Matrix Eigenvalue Problems
• Updating the singular value decomposition