An analogue of the results of Saad and Stewart for harmonic Ritz vectors

Let (λ,x) be an eigenpair of the matrix A of order n and let (μ,u) be a Ritz pair of A with respect to a subspace K. Saad has derived a simple priori error bound for sin∠(x,u) in terms of sin∠(x,K) for A Hermitian. Similar to Saadʹs result, Stewart has got an equally simple inequality for A non-Hermitian. In this paper, let (θ,w) be a harmonic Ritz pair from a subspace K, a similar priori error bound for sin∠(x,w) is established in terms of sin∠(x,K).