Majorization Bounds for Ritz Values of Self-Adjoint Matrices

DOI10.1137/19M1263996zbMath1440.42159arXiv1905.06998OpenAlexW3103920148MaRDI QIDQ5112241

Sebastián Zárate, Pedro G. Massey, Demetrio Stojanoff

Publication date: 28 May 2020

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.06998

zbMATH Keywords

Ritz valuesmajorizationprincipal anglesRayleigh quotients

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) General harmonic expansions, frames (42C15)

Related Items

The spectral spread of Hermitian matrices, Norm inequalities for the spectral spread of Hermitian operators, Sharp Majorization-Type Cluster Robust Bounds for Block Filters and Eigensolvers, Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread

Cites Work

• Unnamed Item
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• The tan \(\theta \) theorem with relaxed conditions
• A note on eigenvalues of perturbed Hermitian matrices
• Cluster-robust accuracy bounds for Ritz subspaces
• On proximity of Rayleigh quotients for different vectors and Ritz values generated by different trial subspaces
• Cluster robust error estimates for the Rayleigh-Ritz approximation II: Estimates for eigenvalues
• Rayleigh--Ritz Majorization Error Bounds of Mixed Type
• Rayleigh–Ritz Majorization Error Bounds with Applications to FEM
• Bounds on Changes in Ritz Values for a Perturbed Invariant Subspace of a Hermitian Matrix
• Quadratic Residual Bounds for the Hermitian Eigenvalue Problem
• Subspace Gap Residuals for Rayleigh–Ritz Approximations
• Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators
• Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra
• Two Subspaces
• The Rotation of Eigenvectors by a Perturbation. III
• Inequalities: theory of majorization and its applications