Rayleigh–Ritz Majorization Error Bounds with Applications to FEM

DOI10.1137/08072574XzbMath1201.65054arXivmath/0701784WikidataQ56001652 ScholiaQ56001652MaRDI QIDQ3584172

Andrew V. Knyazev, Merico E. Argentati

Publication date: 19 August 2010

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

Full work available at URL: https://arxiv.org/abs/math/0701784

zbMATH Keywords

eigenvaluefinite element methodperturbationerror analysisprojectioninner product spaceRitz valuesHermitian matrixRayleigh-Ritz methodmajorizationsubspacesanglesmembrane vibrationmultiplicative boundsgeneralizations for Hilbert spacesHermitian operator \(A\)relative error bounds

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Vibrations in dynamical problems in solid mechanics (74H45) Finite element methods applied to problems in solid mechanics (74S05) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Inequalities involving eigenvalues and eigenvectors (15A42) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Hermitian, skew-Hermitian, and related matrices (15B57) Spectrum, resolvent (47A10) Numerical computation of matrix norms, conditioning, scaling (65F35) Membranes (74K15) Numerical solutions to equations with linear operators (65J10)

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