On Eigenvalue and Eigenvector Estimates for Nonnegative Definite Operators - Grubis ic, Luka (SIAM journal on matrix analysis and applications, 2006)
We present a perturbation approach to the Rayleigh-Ritz approximations in the sense of Davis, Kahan, and Weinberger. We restrict ourselves to nonnegative definite self-adjoint operators and obtain sharp bounds of relative type for both eigenvalues and eigenvectors. The operators are allowed to have nontrivial null-spaces, and the test spaces need not be contained in the domain of the considered operator.