Rayleigh--Ritz Approximation For the Linear Response Eigenvalue Problem

DOI10.1137/130946563zbMath1305.65126OpenAlexW2050538573MaRDI QIDQ2923370

Lei-Hong Zhang, Ren-Cang Li, Jungong Xue

Publication date: 15 October 2014

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

Full work available at URL: https://semanticscholar.org/paper/05c75788169571d1bb270dff957e6b58a83441a3

zbMATH Keywords

error boundsRayleigh-Ritz approximationeigenvalue approximationrandom phase approximationlinear response eigenvalue problemdeflating subspacesmallest positive eigenvaluecanonical angles

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators (34L16) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (6)

A projected preconditioned conjugate gradient method for the linear response eigenvalue problem ⋮ A block Lanczos method for the linear response eigenvalue problem ⋮ Rayleigh-Ritz majorization error bounds for the linear response eigenvalue problem ⋮ Error bounds for approximate deflating subspaces for linear response eigenvalue problems ⋮ Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem ⋮ Thick restarting the weighted harmonic Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem

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