Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators

DOI10.1137/120884468zbMath1272.15014arXiv1207.3240OpenAlexW1988591471WikidataQ59695782 ScholiaQ59695782MaRDI QIDQ5300554

Peizhen Zhu, Merico E. Argentati, Andrew V. Knyazev

Publication date: 27 June 2013

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

Full work available at URL: https://arxiv.org/abs/1207.3240

zbMATH Keywords

eigenvaluea priori boundsperturbationHilbert spaceerror analysisspectrumRayleigh quotientanglesa posteriori boundsself-adjoint bounded operator

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Spectrum, resolvent (47A10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (6)

The spectral spread of Hermitian matrices ⋮ Rayleigh--Ritz Majorization Error Bounds of Mixed Type ⋮ Fast computation of error bounds for all eigenpairs of a Hermitian and all singular pairs of a rectangular matrix with emphasis on eigen- and singular value clusters ⋮ Majorization Bounds for Ritz Values of Self-Adjoint Matrices ⋮ Absolute Variation of Ritz Values, Principal Angles, and Spectral Spread ⋮ High order approximations of the operator Lyapunov equation have low rank

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