Journal title
Mathematics of Computation
DOI
10.1090/mcom/3519
Issue
324
Volume
89
Last updated
2024-03-24T17:56:34.663+00:00
Page
1843-1866
Abstract
We derive sharp bounds for the accuracy of approximate eigenvectors (Ritz vectors) obtained by the Rayleigh-Ritz process for symmetric eigenvalue problems. Using information that is available or easy to estimate, our bounds improve the classical Davis-Kahan theorem by a factor that can be arbitrarily large, and can give nontrivial information even when the sinθ theorem suggests that a Ritz vector might have no accuracy at all. We also present extensions in three directions, deriving error bounds for invariant subspaces, singular vectors and subspaces computed by a (Petrov-Galerkin) projection SVD method, and eigenvectors of self-adjoint operators on a Hilbert space.
Symplectic ID
1080376
Submitted to ORA
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Publication type
Journal Article
Publication date
29 Jan 2020