Angles between infinite dimensional subspaces with applications to the Rayleigh-Ritz and alternating projectors methods

DOI10.1016/j.jfa.2010.05.018zbMath1202.47007arXiv0705.1023OpenAlexW2102867755WikidataQ56001654 ScholiaQ56001654MaRDI QIDQ990147

Abram Jujunashvili, Andrew V. Knyazev, Merico E. Argentati

Publication date: 6 September 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.1023

zbMATH Keywords

gapHilbert spacedomain decompositionisometryRayleigh-Ritz methodpolar decompositionconjugate gradientcanonical correlationsanglesalternating projectors

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Invariant subspaces of linear operators (47A15) Applications of operator theory in numerical analysis (47N40)

Related Items

Principal invariant subspaces theorems ⋮ General explicit descriptions for intertwining operators and direct rotations of two orthogonal projections ⋮ Rayleigh--Ritz Majorization Error Bounds of Mixed Type ⋮ Comparing the methods of alternating and simultaneous projections for two subspaces ⋮ On angles, projections and iterations ⋮ Stable determination of an anisotropic inclusion in the Schrödinger equation from local Cauchy data ⋮ Counting collisions in an \(N\)-billiard system using angles between collision subspaces ⋮ Saddle point problems, Bott-Duffin inverses, abstract splines and oblique projections ⋮ On angles and distances between subspaces ⋮ A posteriori error estimates for elliptic eigenvalue problems using auxiliary subspace techniques ⋮ On principal invariant subspaces ⋮ Spectral discretization errors in filtered subspace iteration ⋮ High order approximations of the operator Lyapunov equation have low rank

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